Victor Kac

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Victor Kac is affiliated with the following schools: Moscow State University, Massachusetts Institute of Technology, Moscow State University

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Victor Kac

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#30

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Algebra

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#12

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#369

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#107

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Mathematics

Victor Kac's Degrees

PhD Mathematics Moscow State University

Why Is Victor Kac Influential?

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According to Wikipedia, Victor Gershevich Kac is a Soviet and American mathematician at MIT, known for his work in representation theory. He co-discovered Kac–Moody algebras, and used the Weyl–Kac character formula for them to reprove the Macdonald identities. He classified the finite-dimensional simple Lie superalgebras, and found the Kac determinant formula for the Virasoro algebra. He is also known for the Kac–Weisfeiler conjectures with Boris Weisfeiler.

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Victor Kac's Published Works

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Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Infinite dimensional Lie algebras: Frontmatter (1990) (1538)
Vertex algebras for beginners (1997) (1350)
Basic representations of affine Lie algebras and dual resonance models (1980) (820)
Bombay Lectures On Highest Weight Representations Of Infinite Dimensional Lie Algebras (1983) (718)
Infinite-dimensional Lie algebras, theta functions and modular forms (1984) (714)
Infinite Dimensional Lie Algebras (1983) (626)
Representations of classical lie superalgebras (1978) (533)
Infinite root systems, representations of graphs and invariant theory (1980) (507)
A sketch of Lie superalgebra theory (1977) (430)
SIMPLE IRREDUCIBLE GRADED LIE ALGEBRAS OF FINITE GROWTH (1968) (379)
Structure of representations with highest weight of infinite-dimensional Lie algebras☆ (1979) (363)
Representations of quantum groups at roots of 1 (1992) (356)
Some remarks on nilpotent orbits (1980) (355)
Spin and wedge representations of infinite-dimensional Lie algebras and groups. (1981) (306)
Modular invariant representations of infinite-dimensional Lie algebras and superalgebras. (1988) (302)
Infinite-dimensional algebras, Dedekind's η-function, classical möbius function and the very strange formula (1978) (291)
Modular and conformal invariance constraints in representation theory of affine algebras (1988) (271)
Infinite flag varieties and conjugacy theorems. (1983) (259)
Quasifinite highest weight modules over the Lie algebra of differential operators on the circle (1993) (257)
Moduli spaces of curves and representation theory (1988) (256)
Contravariant form for infinite-dimensional Lie algebras and superalgebras (1979) (252)
Integrable Highest Weight Modules over Affine Superalgebras and Number Theory (1994) (244)
Quantum Reduction for Affine Superalgebras (2003) (241)
Structure theory of finite conformal algebras (1998) (240)
Characters and fusion rules forW-algebras via quantized Drinfeld-Sokolov reduction (1992) (233)
Finite vs affine W-algebras (2005) (230)
Root systems, representations of quivers and invariant theory (1983) (218)
Quantum reduction and representation theory of superconformal algebras (2003) (207)
Symmetric Quantum Calculus (2002) (207)
W_{1+\infty} and W(gl_N) with central charge N (1994) (193)
Classification of simple z-graded lie superalgebras and simple jordan superalgebras (1977) (193)
Realization of the basic representations of the Euclidean Lie algebras (1981) (187)
On integral representations of $q$-gamma and $q$-beta functions (2003) (184)
Characters of typical representations of classical lie superalgebras (1977) (184)
The n-Component KP Hierarchy and Representation Theory (1993) (178)
Classification of Infinite-Dimensional Simple Linearly Compact Lie Superalgebras☆ (1998) (177)
Infinite root systems, representations of graphs and invariant theory, II (1982) (174)
Cohomology of Conformal Algebras (1998) (172)
Integrable Highest Weight Modules over Affine Superalgebras and Appell's Function (2000) (171)
Geometric interpretation of the partition function of 2D gravity (1991) (168)
Theory of Finite Pseudoalgebras (2000) (155)
Conformal Modules (1997) (150)
Representation theory of the vertex algebraW1+∞ (1996) (146)
Vertex Operator Superalgebras and Their Representations (1993) (138)
Defining relations of certain infinite-dimensional groups (1984) (137)
Field Algebras (2002) (131)
Poisson vertex algebras in the theory of Hamiltonian equations (2009) (130)
Classification of modular invariant representations of affine algebras (1989) (129)
Structure of some categories of representations of infinite-dimensional lie algebras (1982) (128)
Description of Filtered Lie Algebras with which Graded Lie Algebras of CARTAN Type are Associated (1974) (123)
Formal distribution algebras and conformal algebras (1997) (121)
Regular Functions on Certain Infinite-dimensional Groups (1983) (115)
A new class of unitarizable highest weight representations of infinite-dimensional Lie algebras, II (1989) (110)
112 CONSTRUCTIONS OF THE BASIC REPRESENTATION OF THE LOOP GROUP OF E(8) (1986) (108)
Infinite Dimensional Lie Algebras: An Introduction (1988) (108)
Torsion in cohomology of compact Lie groups and Chow rings of reductive algebraic groups (1985) (107)
On defining relations of certain infinite-dimensional Lie algebras (1981) (105)
Vacuum structure in supersymmetric Yang--Mills theories with any gauge group (1999) (101)
Coadjoint action of a semi-simple algebraic group and the center of the enveloping algebra in characteristic p (1976) (97)
A newN= 6 superconformal algebra (1997) (91)
Laplace operators of infinite-dimensional Lie algebras and theta functions. (1984) (88)
Superconformal current algebras and their unitary representations (1986) (87)
Classification of finite simple Lie conformal superalgebras (2001) (86)
Constructing Groups Associated to Infinite-Dimensional Lie Algebras (1985) (85)
Affine Orbifolds and Rational Conformal Field Theory Extensions of W1+∞ (1996) (85)
Some problems on infinite dimensional lie algebras and their representations (1982) (84)
Some quantum analogues of solvable Lie groups (1993) (84)
The geometry of spinors and the multicomponent BKP and DKP hierarchies (1997) (79)
Superconformal current algebras and their unitary representations (1985) (78)
Quasifinite Representations of Classical Lie Subalgebras of W1 (1998) (78)
On simplicity of vacuum modules (2006) (77)
The idea of locality (1997) (73)
Normalized vacuum states in N=4 supersymmetric Yang–Mills quantum mechanics with any gauge group (1999) (73)
The in?nite wedge representation and the reciprocity law for algebraic curves (1987) (72)
On automorphisms of Kac-Moody algebras and groups (1992) (70)
Twisted Modules over Lattice Vertex Algebras (2004) (70)
Affine Lie algebras and Hecke modular forms (1980) (70)
Extensions of Conformal Modules (1997) (69)
Some remarkable degenerations of quantum groups (1993) (68)
Classification of linearly compact simple Jordan and generalized Poisson superalgebras (2006) (67)
On Rationality of W-algebras (2007) (67)
Branching functions for winding subalgebras and tensor products (1990) (66)
An elucidation of "Infinite dimensional algebras. . .and the very strange formula (1980) (66)
Structure of some ℤ-graded lie superalgebras of vector fields (1999) (64)
q-Gamma and q-Beta Functions (2002) (61)
Non-local Poisson structures and applications to the theory of integrable systems (2012) (58)
On the classification of subalgebras of CendN and gcN (2003) (57)
Classification of Simple Linearly Compact n-Lie Superalgebras (2009) (55)
Unitarizable highest weight representations of the Virasoro, Neveu-Schwarz and Ramond algebras (1986) (55)
Simple graded algebras of finite growth (1967) (54)
Superconformal algebras and transitive group actions on quadrics (1997) (54)
Infinite dimensional groups with applications (1985) (53)
Finite linear groups whose ring of invariants is a complete intersection (1982) (52)
Finite-dimensional representations of quantum affine algebras at roots of unity (1994) (48)
Solitons in Affine and Permutation Orbifolds (2003) (47)
Conformal embeddings of affine vertex algebras in minimal W-algebras I: Structural results (2016) (46)
EXPONENTIALS IN LIE ALGEBRAS OF CHARACTERISTIC p (1971) (46)
Γ-conformal algebras (1997) (46)
Classification of supersymmetries (2003) (46)
Classical $${\mathcal{W}}$$W -Algebras and Generalized Drinfeld-Sokolov Bi-Hamiltonian Systems Within the Theory of Poisson Vertex Algebras (2012) (45)
Representations of affine superalgebras and mock theta functions. III (2013) (45)
ON THE CLASSIFICATION OF SIMPLE LIE ALGEBRAS OVER A FIELD OF NONZERO CHARACTERISTIC (1970) (45)
On E 10 (1988) (43)
Corrigendum to ¿Quantum reduction and representation theory of superconformal algebras¿¿: [Adv. Math. 185 (2004) 400¿458] (2005) (43)
Freely Generated Vertex Algebras and Non–Linear Lie Conformal Algebras (2003) (42)
The variational Poisson cohomology (2011) (42)
Lie Theory and Geometry (1994) (42)
Graded Simple Jordan Superalgebras of Growth One (2001) (42)
On geometric invariant theory for infinite-dimensional groups (1987) (41)
Addendum: Generalized Spencer Cohomology and Filtered Deformations of Z-graded Lie Superalgebras (1998) (39)
Unitary structure in representations of infinite-dimensional groups and a convexity theorem (1984) (39)
Lie Conformal Algebra Cohomology and the Variational Complex (2008) (38)
Structure of classical (finite and affine) W-algebras (2014) (37)
Polynomial tau-functions of BKP and DKP hierarchies (2018) (37)
A remark on boundary level admissible representations (2016) (37)
Supersymmetric Vertex Algebras (2006) (36)
Conformal embeddings of affine vertex algebras in minimal W-algebras II: decompositions (2016) (33)
The n-Compo ne nt KP Hierarchy a nd Represe ntatio n Theory (1993) (32)
Highest Weight Representations of Infinite-Dimensional Lie Algebras (2010) (31)
Quasifinite highest weight modules over the Lie algebra of matrix differential operators on the circle (1998) (31)
Geometric interpretation of the partition function of 2 D gravity (2002) (31)
Quantum Reduction in the Twisted Case (2004) (30)
Representations of the Exceptional Lie Superalgebra E(3,6) II: Four Series of Degenerate Modules (2000) (30)
On complete reducibility for infinite-dimensional Lie algebras (2009) (30)
Representations of simple finite Lie conformal superalgebras of type $W$ and $S$. (2006) (30)
Classical W-algebras within the theory of Poisson vertex algebras (2014) (29)
Finite vs. Infinite Decompositions in Conformal Embeddings (2015) (28)
Structure theory of finite Lie conformal superalgebras (2004) (27)
Some remarks on representations of quivers and infinite root systems (1980) (27)
On the classification of subalgebras of Cend_N and gc_N (2002) (27)
Equivalence of formulations of the MKP hierarchy and its polynomial tau-functions (2018) (27)
Characters of (relatively) integrable modules over affine Lie superalgebras (2014) (26)
Conformal Embeddings and Simple Current Extensions (2012) (26)
Representations of the exceptional lie superalgebraE(3, 6) I: Degeneracy conditions (2000) (26)
Classification of Linearly Compact Simple Rigid Superalgebras (2009) (26)
Infinite-dimensional primitive linearly compact Lie superalgebras (2005) (25)
Simple lie groups and the legendre symbol (1981) (25)
Classification of Finite Irreducible Modules over the Lie Conformal Superalgebra CK6 (2011) (25)
Double Poisson vertex algebras and non-commutative Hamiltonian equations (2014) (24)
Unitary Quasi-finite Representations of W∞ (2000) (24)
A New Scheme of Integrability for (bi)Hamiltonian PDE (2015) (24)
Infinite dimensional Lie algebras and groups : proceedings of the conference held at CIRM, Luminy, Marseille, July 4-8, 1988 (1989) (24)
Polynomial tau-functions of the KP, BKP, and the s-component KP hierarchies (2020) (24)
Generalized Vertex Algebras (2006) (23)
Multiplets of representations, twisted Dirac operators and Vogan's conjecture in affine setting (2007) (23)
Dirac Reduction for Poisson Vertex Algebras (2013) (23)
Introduction to vertex algebras, Poisson vertex algebras, and integrable Hamiltonian PDE (2015) (22)
Classical Affine $${\mathcal{W}}$$W-Algebras for $${\mathfrak{gl}_N}$$glN and Associated Integrable Hamiltonian Hierarchies (2015) (21)
An Application of Collapsing Levels to the Representation Theory of Affine Vertex Algebras (2018) (21)
Rational matrix pseudodifferential operators (2012) (20)
Irreducible modules over finite simple Lie pseudoalgebras II. Primitive pseudoalgebras of type K (2004) (20)
Irreducible modules over finite simple Lie conformal superalgebras of type K (2010) (20)
Erratum: Conformal modules (1998) (20)
Complexes of modules over exceptional Lie superalgebras E(3,8) and E(5,10) (2001) (20)
Cyclic elements in semisimple lie algebras (2012) (19)
Some algebraic properties of differential operators (2012) (18)
Subalgebras of gc N and Jacobi Polynomials (2001) (18)
Finite growth representations of infinite Lie conformal algebras (2002) (18)
On classification of poisson vertex algebras (2010) (17)
Errata to "Structure of Some ℤ-graded Lie Superalgebras of Vector Fields'' (2004) (17)
Denominator identities for finite-dimensional Lie superalgebras and Howe duality for compact dual pairs (2011) (16)
Essential Variational Poisson Cohomology (2011) (16)
Classical Affine $${\mathcal W}$$W-Algebras and the Associated Integrable Hamiltonian Hierarchies for Classical Lie Algebras (2017) (15)
Classical Affine W -Algebras and the Associated Integrable Hamiltonian Hierarchies for Classical Lie Algebras (2018) (14)
Decomposition rules for conformal pairs associated to symmetric spaces and abelian subalgebras of Z2-graded Lie algebras (2005) (14)
Classical $${\mathcal{W}}$$W-Algebras and Generalized Drinfeld–Sokolov Hierarchies for Minimal and Short Nilpotents (2013) (13)
An operadic approach to vertex algebra and Poisson vertex algebra cohomology (2018) (13)
Good Gradings of Simple Lie Algebras (2003) (12)
On exceptional nilpotents in semisimple Lie algebras (2008) (12)
A Lax type operator for quantum finite W-algebras (2017) (12)
Extensions of Neveu–Schwarz conformal modules (2000) (12)
On the super-KP hierachy (1996) (12)
Some remarks on non-commutative principal ideal rings (2013) (11)
Non-local Hamiltonian structures and applications to the theory of integrable systems I (2012) (11)
Automorphisms and Forms of Simple Infinite-Dimensional Linearly Compact Lie Superalgebras (2006) (11)
Euler-Maclaurin Formula (2002) (11)
Differential conformal superalgebras and their forms (2008) (11)
REPRESENTATIONS OF THE EXCEPTIONAL LIE SUPERALGEBRA E(3,6) III: CLASSIFICATION OF SINGULAR VECTORS (2003) (11)
IRREDUCIBLE MODULES OVER FINITE SIMPLE LIE PSEUDOALGEBRAS I. PRIMITIVE PSEUDOALGEBRAS OF TYPE W AND S BOJKO BAKALOV, ALESSANDRO D’ANDREA, AND VICTOR G. KAC (2011) (11)
On the structure of quantum vertex algebras (2019) (10)
Representation theory of the vertex algebra $W_{1 + \infty}$ (1995) (10)
On the classification of non-equal rank affine conformal embeddings and applications (2017) (10)
Finite W-algebras for glN (2016) (9)
Algebras, Representations and Applications (2009) (9)
Classification of linearly compact simple algebraic N = 6 3-algebras (2011) (9)
A remark on the Conway-Norton conjecture about the "Monster" simple group. (1980) (9)
On Characters of Irreducible Highest Weight Modules of Negative Integer Level over Affine Lie Algebras (2017) (9)
Real and imaginary roots (1983) (9)
Computation of cohomology of Lie conformal and Poisson vertex algebras (2019) (8)
A New Approach to the Lenard–Magri Scheme of Integrability (2013) (8)
Poisson Structure for Restricted Lie Algebras (2000) (8)
Classification of linearly compact simple Nambu-Poisson algebras (2015) (8)
Erratum to: Classical W-Algebras and Generalized Drinfeld–Sokolov Hierarchies for Minimal and Short Nilpotents (Commun. Math. Phys., (2014), 331, (623-676), 10.1007/s00220-014-2049-2) (2014) (7)
Poisson Λ-brackets for Differential–Difference Equations (2018) (7)
Singular Degree of a Rational Matrix Pseudodifferential Operator (2013) (7)
Computation of cohomology of vertex algebras (2020) (7)
On simplicity of certain infinite dimensional Lie algebras (1980) (7)
A differential analog of a theorem of Chevalley (2001) (6)
A CHARACTERIZATION OF MODIFIED MOCK THETA FUNCTIONS (2015) (6)
Lie conformal superalgebras and duality of modules over linearly compact Lie superalgebras (2020) (6)
Dirac operators and the very strange formula for Lie superalgebras (2013) (6)
Trace functions of the parafermion vertex operator algebras (2018) (6)
Classification of infinite-dimensional simple groups of supersymmetries and quantum field theory (1999) (6)
Integrability of Dirac reduced bi-Hamiltonian equations (2014) (6)
Calculus structure on the Lie conformal algebra complex and the variational complex (2010) (6)
Chiral Versus Classical Operad (2020) (6)
On integrability of some bi-Hamiltonian two field systems of partial differential equations (2014) (6)
REPRESENTATIONS OF AFFINE SUPERALGEBRAS AND MOCK THETA FUNCTIONS (2014) (6)
SEMISIMPLE CYCLIC ELEMENTS IN SEMISIMPLE LIE ALGEBRAS (2019) (5)
EXPONENTIALS IN LIE ALGEBRAS OF CHARACTERISTIC ρ (2005) (5)
Classification of linearly compact simple N=6 3-algebras (2010) (5)
Local and Non-local Multiplicative Poisson Vertex Algebras and Differential-Difference Equations (2018) (5)
Chiral vs classical operad (2018) (5)
Generalized Taylor’s Formula for Polynomials (2002) (5)
Polynomial Tau-Functions for the Multicomponent KP Hierarchy (2019) (5)
Poisson Vertex Algebra Cohomology and Differential Harrison Cohomology (2019) (5)
Classical and variational Poisson cohomology (2021) (4)
p ̲ -reduced Multicomponent KP hierarchy and classical W -algebras W ( gl N , p ̲ ) (2019) (4)
On the Cachazo-Douglas-Seiberg-Witten conjecture for simple Lie algebras (2003) (4)
Sums of Powers (2002) (4)
with central chargeN (1995) (4)
On the Kernel of the affine Dirac operator (2008) (4)
Classification of Degenerate Verma Modules for E(5, 10) (2020) (4)
Characters of highest weight modules over affine Lie algebras are meromorphic functions (2007) (4)
Simple Jordan conformal superalgebras (2008) (4)
Non-negative integer linear congruences (2005) (4)
Quasifinite representations of classical Lie subalgebras of W (1+infinity) (1998) (4)
SUSY Lattice Vertex Algebras (2007) (4)
Classical W-algebras and Drinfeld-Sokolov bi-Hamiltonian systems within the theory of Poisson vertex algebras (2012) (3)
Corrections to the Paper "description of Filtered Lie Algebras with which Graded Lie Algebras of CARTAN Type are Associated" (1976) (3)
Representations of superconformal algebras and mock theta functions (2017) (3)
INTEGRABILITY OF CLASSICAL AFFINE W-ALGEBRAS (2020) (3)
Algebraic vs physical N = 6 3-algebras (2013) (3)
Corrections to the book ``Vertex algebras for beginners'', second edition, by Victor Kac (1999) (3)
Multicomponent KP type hierarchies and their reductions, associated to conjugacy classes of Weyl groups of classical Lie algebras (2023) (2)
Infinite dimensional Lie algebras: Twisted Affine Algebras and Finite Order Automorphisms (1990) (2)
Integrable triples in semisimple Lie algebras (2020) (2)
Non-local Poisson structures and applications to the theory of integrable systems (2013) (2)
Invariant Hermitian forms on vertex algebras (2020) (2)
Lecture 16 — Root Systems and Root Lattices (2010) (2)
Classification of Finite Irreducible Modules over the Lie Conformal Superalgebra CK[subscript 6] (2012) (2)
Yangians versus minimal W-algebras: A surprising coincidence (2020) (2)
Denominator formulas for Lie superalgebras (extended abstract) (2010) (2)
Kostant Pairs of Lie Type and Conformal Embeddings (2018) (2)
Classification of Finite Irreducible Modules over the Lie Conformal Superalgebra CK6 (2012) (2)
q-Derivative and h-Derivative (2002) (2)
Erratum: ``Superconformal current algebras and their unitary representations'' (1986) (2)
Corrigendum to “Multiplets of representations, twisted Dirac operators and Vogan's conjecture in affine setting” [Adv. Math. 217 (6) (2008) 2485–2562] (2019) (2)
Highest weight modules over the Lie algebra g(A) (1983) (1)
Quasifinite Representations of W ∞ (1999) (1)
$$\underline{p}$$-reduced Multicomponent KP Hierarchy and Classical $$\mathcal {W}$$-algebras $$\mathcal {W}(\mathfrak {gl}_N,\underline{p})$$ (2020) (1)
Infinite dimensional Lie algebras: Integrable Representations of Kac–Moody Algebras and the Weyl Group (1990) (1)
Correction to: INTEGRABILITY OF CLASSICAL AFFINE W-ALGEBRAS (2021) (1)
Symmetries, Differential Equations and Applications (2018) (1)
Integrable highest weight modules over affine Lie algebras. Application to η-function identities (1983) (1)
SOME QUANTUM ANALOGUES OF SOLVABLE LIE (1992) (1)
The stability of vacua in two-dimensional gauge theory (2000) (1)
Classification of S up er symmetries (2002) (1)
On Lax operators (2021) (1)
An operadic approach to vertex algebra and Poisson vertex algebra cohomology (2019) (1)
On Dynkin Gradings in Simple Lie Algebras (2018) (1)
Complexes of Modules over Exceptional Lie (2002) (1)
Yangians vs minimal W-algebras: a surprizing coincidence (2019) (1)
Infinite dimensional Lie algebras: Conference Proceedings and Collections of Papers (1990) (1)
Infinite dimensional Lie algebras: Real and Imaginary Roots (1990) (1)
Unitarity of Minimal W-Algebras and Their Representations I (2022) (1)
Characters of (relatively) integrable modules over affine Lie superalgebras (2015) (1)
Erratum to: Classical $${\mathcal {W}}$$W-Algebras and Generalized Drinfeld–Sokolov Hierarchies for Minimal and Short Nilpotents (2015) (0)
Ju n 20 12 Rational matrix pseudodifferential operators (2012) (0)
Integrable highest weight modules: the weight system, the contravariant Hermitian form and the restriction problem (1983) (0)
Differential operators in the classification of simple modular Lie algebras (2016) (0)
O ct 2 01 1 Classification of finite irreducible modules over the Lie conformal superalgebra CK 6 (2011) (0)
Infinite dimensional Lie algebras: Integrable Highest-Weight Modules: the Character Formula (1990) (0)
Infinite dimensional Lie algebras: The Principal and Homogeneous Vertex Operator Constructions of the Basic Representation. Boson–Fermion Correspondence. Application to Soliton Equations (1990) (0)
Affine Lie algebras: the realization (case k=2 or 3). Application to the classification of finite order automorphisms (1983) (0)
BASICITY AND UNICELLULARITY OF WEIGHTED SHIFT OPERATORS (2017) (0)
Wightman axioms and vertex algebras (1998) (0)
Workshop on “ Geometry and Representation Theory ” January 16 – 27 , 2017 organized by (2017) (0)
Infinite dimensional Lie algebras: Integrable Highest-Weight Modules over Affine Algebras. Application to η-Function Identities. Sugawara Operators and Branching Functions (1990) (0)
Èrnest Borisovich Vinberg (2021) (0)
v 2 1 2 Se p 19 97 Conformal Modules by (2008) (0)
Lecture 6 — Generalized Eigenspaces & Generalized Weight Spaces (2010) (0)
q-Taylor’s Formula for Formal Power Series and Heine’s Binomial Formula (2002) (0)
Quasifinite representations of W_{\infty} (1999) (0)
Calculus of formal distributions (1998) (0)
The generalized Giambelli formula and polynomial KP and CKP tau-functions (2022) (0)
A.: Representations of the exceptional Lie superalgebra E(3,6) III: Classification of singular vectors, in preparation (2008) (0)
Integrable Hamiltonian Hierarchies for Classical Lie Algebras (2018) (0)
1 2 Fe b 20 04 Solitons in Affine and Permutation Orbifolds (2008) (0)
Infinite dimensional Lie algebras: Highest-Weight Modules over Kac–Moody Algebras (1990) (0)
The invariant bilinear form and the generalized Casimir operator (1983) (0)
A NOTE ON 2-DIMENSIONAL ARITHMETIC SYMBOLS ON Gl ( n , Σ S ) (2007) (0)
A CHARACTERIZATION OF MODIFIED MOCK THETA FUNCTIONS (2016) (0)
Infinite dimensional Lie algebras: Integrable Highest-Weight Modules: the Weight System and the Unitarizability (1990) (0)
q-Hypergeometric Functions and Heine’s Formula (2002) (0)
q-Analogue of (x − a)n, n an Integer, and q-Derivatives of Binomials (2002) (0)
Classical Partition Function and Euler’s Product Formula (2002) (0)
ON COMPLETE REDUCIBILTY FOR INFINITE-DIMENSIONAL LIE ALGEBRAS (2010) (0)
Infinite dimensional Lie algebras: The Invariant Bilinear Form and the Generalized Casimir Operator (1990) (0)
Classification of Linearly Compact Simple Rigid (2018) (0)
A Lie conformal superalgebra and duality of representations for E(4,4) (2023) (0)
Some properties of generalized Cartan matrices (1983) (0)
Affine Lie algebras: the realization (case k=1) (1983) (0)
Affine Lie algebras, theta functions and modular forms (1983) (0)
SEMISIMPLE CYCLIC ELEMENTS IN SEMISIMPLE LIE ALGEBRAS (2020) (0)
Affine Lie algebras: the normalized invariant bilinear form, the root system and the Weyl group (1983) (0)
Lecture 10 — Trace Form & Cartan ’ s criterion (2010) (0)
Equivalence of formulations of the MKP hierarchy and its polynomial tau-functions (2018) (0)
A New Approach to the Lenard–Magri Scheme of Integrability (2014) (0)
A ] 4 F eb 2 00 6 Generalized Vertex Algebras (2006) (0)
Dirac Reduction for Poisson Vertex Algebras (2014) (0)
A New Scheme of Integrability for (bi)Hamiltonian PDE (2016) (0)
q-Trigonometric Functions (2002) (0)
The principal realization of the basic representation. Application to the KdV-type hierarchies of non-linear partial differential equations (1983) (0)
Orbifolds of Lattice Vertex Algebras (2022) (0)
Communications in Mathematical Physics Classification of Finite Irreducible Modules over the Lie Conformal Superalgebra C K 6 (0)
Spin and . wedge representations of infinite-dimensional Lie . algebras . and groups (0)
Infinite dimensional Lie algebras and local von Neumann algebras in CFT (2007) (0)
Denominator identities for finite-dimensional Lie superalgebras and Howe duality for compact dual pairs (2012) (0)
90 19 v 2 2 4 Ja n 20 00 Extensions of Conformal Modules by (2018) (0)
Examples of vertex algebras and their applications (1998) (0)
Defining relations for minimal unitary quantum affine W-algebras (2023) (0)
The generalized Giambelli formula and polynomial CKP tau-functions (2022) (0)
Integrable representations and the Weyl group of a Kac-Moody algebra (1983) (0)
Аскар Серкулович Джумадильдаев (к шестидесятилетию со дня рождения)@@@Askar Serkulovich Dzhumadil'daev (on his 60th birthday) (2017) (0)
Normal forms of nilpotent elements in semisimple Lie algebras (2021) (0)
Integrable highest weight modules: the character formula (1983) (0)
The variational Poisson cohomology (2013) (0)
A remark on the Conway-Norton conjecture about the "Monster" simple group (0)
Essential Variational Poisson Cohomology (2012) (0)
Explicit Formulas for Sums of Two and of Four Triangular Numbers (2002) (0)
Adler-Oevel-Ragnisco type operators and Poisson vertex algebras (2022) (0)
Alexandre Mikhailovich Vinogradov (2020) (0)
Infinite dimensional Lie algebras: Affine Algebras as Central Extensions of Loop Algebras (1990) (0)
On Free Field Realization of Quantum Affine W-Algebras (2021) (0)
2 M ay 2 01 2 Cyclic elements in semisimple Lie algebras (0)
UNITARIZABLE HIGN~ST WEIGHT REPRESENTATIONS OF THE VIRASORO, NEVEU-SCh~ARZ AND RAMONDALGEBRAS (0)
Infinite dimensional Lie algebras: A Classification of Generalized Cartan Matrices (1990) (0)
On Lax operators (2021) (0)
Infinite dimensional Lie algebras: Affine Algebras, Theta Functions, and Modular Forms (1990) (0)
A Lax type operator for quantum finite W-algebras (2018) (0)
Infinite dimensional Lie algebras: Affine Algebras: the Normalized Invariant Form, the Root System, and the Weyl Group (1990) (0)
Bernoulli Polynomials and Bernoulli Numbers (2002) (0)
Rational matrix pseudodifferential operators (2013) (0)
Non-linear Lie Conformal algebras (2004) (0)
Subregular nilpotent orbits and explicit character formulas for modules over affine Lie algebras (2022) (0)
q-Binomial Coefficients and Linear Algebra over Finite Fields (2002) (0)
Local and Non-local Multiplicative Poisson Vertex Algebras and Differential-Difference Equations (2019) (0)
Special issue in honour of Ernest Borisovich Vinberg (2007) (0)
Erratum to: Classical W\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {W}}$$\end{document}-Algebras and Gen (2014) (0)
Two Euler’s Identities and Two q-Exponential Functions (2002) (0)
70 90 08 v 1 2 S ep 1 99 7 The idea of locality (1997) (0)
Classical W\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{W}}$$\end{document}-Algebras and Generalized Drin (2014) (0)
a simple Lie algebra of classical type and semisimple (2018) (0)
Victor Kac Interview (2010) (0)
Infinite dimensional Lie algebras: References (1990) (0)
Lecture 2 — Some Sources of Lie Algebras (2010) (0)
Infinite dimensional Lie algebras: Basic Definitions (1990) (0)
Finite vs. Infinite Decompositions in Conformal Embeddings (2016) (0)
q-Taylor’s Formula for Polynomials (2002) (0)
More on Heine’s Formula and the General Binomial (2002) (0)
Non-Archimedean Vertex Algebras (2023) (0)
Unitarity of minimal $W$-algebras (2020) (0)
Fundamental Theorem of q-Calculus and Integration by Parts (2002) (0)
Lecture 21 — The Weyl Group of a Root System (2010) (0)
Jacobi’s Triple Product Identity (2002) (0)
Corrections to the Paper of B. YU. VEISFEILER and V. G. KAC (1995) (0)
Gauss’s Binomial Formula and a Noncommutative Binomial Formula (2002) (0)
h-Derivative and h-Integral (2002) (0)
Cyclic elements in semisimple lie algebras (2013) (0)
Properties of q-Binomial Coefficients (2002) (0)
Institute for Mathematical Physics Classiication of Innnite{dimensional Simple Linearly Compact Lie Superalgebras Classiication of Innnite-dimensional Simple Linearly Compact Lie Superalgebras (2009) (0)
On complexity of representations of quivers (2019) (0)
Integrable Hamiltonian Hierarchies (2016) (0)
Ramanujan Product Formula (2002) (0)
Finite vs. W-algebras (2005) (0)
Structure theory of vertex algebras (1998) (0)
Explicit Formulas for Sums of Two and of Four Squares (2002) (0)
On the classification of non-equal rank affine conformal embeddings and applications (2018) (0)
Conformal embeddings of affine vertex algebras in minimal W-algebras II: decompositions (2017) (0)

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