Boris Feigin

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Boris Feigin is affiliated with the following schools: Higher School of Economics, Moscow State University

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Boris Feigin

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According to Wikipedia, Boris Lvovich Feigin is a Russian mathematician. His research has spanned representation theory, mathematical physics, algebraic geometry, Lie groups and Lie algebras, conformal field theory, homological and homotopical algebra.

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Boris Feigin'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

AFFINE KAC-MOODY ALGEBRAS AT THE CRITICAL LEVEL AND GELFAND-DIKII ALGEBRAS (1992) (330)
Verma modules over the virasoro algebra (1983) (326)
Invariant skew-symmetric differential operators on the line and Verma modules over the Virasoro algebra (1982) (326)
Quantization of the Drinfeld-Sokolov reduction (1990) (273)
Gaudin model, Bethe Ansatz and critical level (1994) (273)
A commutative algebra on degenerate CP^1 and Macdonald polynomials (2009) (205)
Quantum-algebras and elliptic algebras (1995) (195)
Quasi-particles models for the representations of Lie algebras and geometry of flag manifold (1993) (162)
Equivariant K-theory of Hilbert schemes via shuffle algebra (2009) (161)
Kazhdan-Lusztig correspondence for the representation category of the triplet W-algebra in logarithmic CFT (2005) (153)
Additive K-theory (1987) (153)
Integrals of motion and quantum groups (1993) (150)
Functional models for representations of current algebras and semi-infinite Schubert cells (1994) (146)
Quantum algebraic approach to refined topological vertex (2011) (132)
On generalized Kostka polynomials and quantum Verlinde rule (1998) (127)
A family of representations of affine Lie algebras (1988) (119)
REPRESENTATIONS OF AFFINE KAC-MOODY ALGEBRAS AND BOSONIZATION (1990) (108)
Homology of the Lie algebra of vector fields on the line (1980) (108)
Instanton Moduli Spaces and Bases in Coset Conformal Field Theory (2011) (108)
Singular vectors in Verma modules over Kac—Moody algebras (1986) (104)
Representations of affine Kac-Moody algebras, bosonization and resolutions (1990) (103)
Equivalence between Chain Categories of Representations of Affine sl(2) and N=2 Superconformal Algebras (1997) (102)
Vector bundles on elliptic curve and Sklyanin algebras (1995) (99)
Quantum continuous gl ∞ : Semiinﬁnite construction of representations (2011) (95)
Gaudin models with irregular singularities (2006) (88)
Notes on Ding-Iohara algebra and AGT conjecture (可積分系数理の多様性--RIMS研究集会報告集) (2011) (86)
Multi-Dimensional Weyl Modules and Symmetric Functions (2002) (86)
Quantum continuous $\mathfrak{gl}_{\infty}$: Semiinfinite construction of representations (2010) (84)
Yangians and cohomology rings of Laumon spaces (2008) (83)
Sklyanin elliptic algebras (1989) (81)
Symmetric polynomials vanishing on the shifted diagonals and Macdonald polynomials (2002) (80)
Additive K-theory and crystalline cohomology (1985) (79)
Super Liouville conformal blocks from $ \mathcal{N} = 2 $ SU(2) quiver gauge theories (2011) (77)
A differential ideal of symmetric polynomials spanned by Jack polynomials at rβ = -(r=1)/(k+1) (2001) (77)
The Annihilating Ideals of Minimal Models (1992) (76)
Quantum toroidal gl 1 ?> and Bethe ansatz (2015) (75)
Quantum continuous gl ∞ : Tensor products of Fock modules and W n -characters (2011) (70)
A Finite Analog of the AGT Relation I: Finite W-Algebras and Quasimaps’ Spaces (2010) (70)
Hochschild cohomology of the Weyl algebra and traces in deformation quantization (2003) (67)
Opers with irregular singularity and spectra of the shift of argument subalgebra (2007) (66)
Representations of quantum toroidal gln (2012) (65)
Resolutions and characters of irreducible representations of the N = 2 superconformal algebra (1998) (65)
COMMUNICATIONS OF THE MOSCOW MATHEMATICAL SOCIETY: The semi-infinite homology of Kac-Moody and Virasoro Lie algebras (1984) (65)
Quantum group representations and the Baxter equation. (1996) (63)
Quantum toroidal $\mathfrak{gl}_{1}$-algebra: Plane partitions (2011) (62)
Quantization of soliton systems and Langlands duality (2007) (61)
The Lie algebras $ \mathfrak{gl}(\lambda)$ and cohomologies of Lie algebras of differential operators (1988) (60)
Branching rules for quantum toroidal gl(n) (2013) (56)
Duality in W-algebras (1991) (55)
Cohomologies of Lie algebras of generalized Jacobi matrices (1983) (54)
Logarithmic CFTs connected with simple Lie algebras (2010) (53)
Quantum continuous $\mathfrak{gl}_{\infty}$: Tensor products of Fock modules and $\mathcal{W}_{n}$-characters (2010) (52)
Coinvariants of nilpotent subalgebras of the Virasoro algebra and partition identities (1993) (52)
Semi-infinite Weil complex and the Virasoro algebra (1991) (51)
Kernel function and quantum algebras (2010) (50)
Cyclic homology of algebras with quadratic relations, universal enveloping algebras and group algebras (1987) (48)
Cohomology of some nilpotent subalgebras of the Virasoro and Kac-Moody Lie algebras (1988) (48)
On algebraic equations satisfied by hypergeometric correlators in WZW models. I (1994) (47)
Cohomologies of the Lie algebra of formal vector fields with coefficients in its adjoint space and variations of characteristic classes of foliations (1974) (42)
Finite Type Modules and Bethe Ansatz for Quantum Toroidal $${\mathfrak{gl}_1}$$gl1 (2016) (41)
Rogers–Ramanujan type identities and Nil-DAHA (2012) (40)
Integrals of motion from quantum toroidal algebras (2017) (40)
Quantized Moduli Spaces of the Bundles on the Elliptic Curve and Their Applications (2001) (39)
Lusztig limit of quantum sl(2) at root of unity and fusion of (1,p) Virasoro logarithmic minimal models (2009) (39)
On algebraic equations satisfied by hypergeometric correlators in WZW models. II (1994) (39)
Free field resolutions in affine Toda field theories (1992) (36)
COMBINATORICS OF THE ŝl 2 SPACES OF COINVARIANTS (1999) (36)
Bosonic Formulas for (k, l)-Admissible Partitions (2001) (36)
Kazhdan--Lusztig correspondence for the representation category of the triplet W-algebra in logarithmic Conformal Field Theory (2005) (35)
On $[A,A]/[A,[A,A]]$ and on a $W_n$-action on the consecutive commutators of free associative algebras (2006) (32)
Spaces of coinvariants and fusion product I. From equivalence theorem to Kostka polynomials (2002) (30)
Free-Field Resolutions of the Unitary N=2 Super-Virasoro Representations (1998) (29)
SEMIINFINITE FLAGS. II. LOCAL AND GLOBAL INTERSECTION COHOMOLOGY OF QUASIMAPS’ SPACES. (1997) (28)
Fermionic Formulas for (k , 3)-admissible Configurations (2002) (28)
Quantum toroidal $\mathfrak{g}{{\mathfrak{l}}_{1}}$ and Bethe ansatz (2015) (27)
Andrews–Gordon type identities from combinations of Virasoro characters (2005) (25)
Form factors of descendant operators: free field construction and reflection relations (2008) (25)
Extended vertex operator algebras and monomial bases (1999) (23)
Separation of variables for Gaudin–Calogero systems (1996) (23)
N = 4 Superconformal Algebras and Diagonal Cosets (2019) (22)
Spaces of coinvariants and fusion product II. sl2 character formulas in terms of Kostka polynomials (2004) (22)
Gelfand–Tsetlin algebras and cohomology rings of Laumon spaces (2008) (22)
Combinatorics and Geometry of Higher Level Weyl Modules (2005) (22)
The Integrals of Motion for the Deformed Virasoro Algebra (2007) (21)
Kac-Moody groups and integrability of soliton equations (1993) (21)
New Trends in Quantum Integrable Systems (2010) (21)
Integrable Sl 2 -modules as Infinite Tensor Products (20)
Fermionic Formulas for Eigenfunctions of the Difference Toda Hamiltonian (2008) (20)
Vertex Operator Algebra Arising from the Minimal Series M(3,p) and Monomial Basis (2000) (20)
Elliptic deformations of current algebras and their representations by difference operators (1997) (19)
Constructions of Sklyanin elliptic algebras and quantumR-Matrices (1993) (19)
Integral Intertwining Operators and Complex Powers of Differential ($q-$Difference) Operators (1993) (18)
Riemann-Roch-Hirzebruch theorem and Topological Quantum Mechanics (2004) (18)
Zhu's algebras, $C_2$-algebras and abelian radicals (2009) (17)
A realization of the modular functor in the space of differentials and the geometric approximation of the moduli space ofG-bundles (1994) (17)
Quantized W-algebra of sl(2,1) : a construction from the quantization of screening operators (1998) (17)
Integrable Hierarchies and Wakimoto Modules (1999) (17)
Principal $\hat{sl}(3)$ subspaces and quantum Toda Hamiltonian (2007) (17)
On the Finitization of the Gordon Identities (2000) (16)
Coupling of Two Conformal Field Theories and Nakajima–Yoshioka Blow-Up Equations (2013) (15)
Massey operations in the cohomology of the infinite dimensional Lie algebra L1 (1988) (15)
On algebraic equations satisfied by correlators in Wess-Zumino-Witten models (1990) (15)
Fermionic formulas for (1,p) logarithmic model characters in \Phi_{2,1} quasiparticle realisation (2007) (15)
Bethe subalgebras of $$U_q(\widehat{\mathfrak {gl}}_n)$$Uq(gl^n) via shuffle algebras (2015) (14)
Bethe subalgebras of Uq ( ̂ gl n ) via shuffle algebras (2015) (14)
Characteristic classes of flags of foliations (1975) (14)
Characters of coinvariants in (1,p) logarithmic models (2008) (14)
Quantized W-algebra of sl(2,1) and quantum parafermions of U_q(sl(2)) (1998) (13)
Cohomology of infinite-dimensional Lie algebras and Laplace operators (1978) (13)
Schubert varieties and the fusion products (2003) (13)
Functional realization of some elliptic Hamiltonian structures and bosonization of the corresponding quantum algebras. (2001) (12)
Difference equations of quantum current operators and quantum parafermion construction (1996) (12)
VOA[M4] (2018) (12)
Invariant differential operators on the line (1979) (12)
Bosonic ghost system and the Virasoro algebra (1990) (12)
Homological realization of restricted Kostka polynomials (2005) (12)
Particle Content of the (k, 3)-configurations (2002) (11)
Q-characters of the tensor products (2002) (11)
COHOMOLOGY OF GROUPS AND ALGEBRAS OF FLOWS (1980) (11)
Conformai Field Theory and Cohomologies of the Lie Algebra of Holomorphic Vector Fields on a Complex Curve (2010) (11)
Symmetric polynomials vanishing on thediagonals shifted by roots of unity (2002) (10)
COMMUNICATIONS OF THE MOSCOW MATHEMATICAL SOCIETY: On the cohomology of certain Lie algebras and superalgebras of vector fields (1982) (10)
Topics in Quantum Groups and Finite-Type Invariants: Mathematics at the Independent University of Moscow (1998) (10)
Towards trigonometric deformation of sl^2 coset VOA (2018) (10)
Urod algebras and Translation of W-algebras (2020) (10)
Affine sl(2|1) and D(2|1;alpha) as Vertex Operator Extensions of Dual Affine sl(2) Algebras (1999) (10)
A Monomial Basis for the Virasoro Minimal Series M(p,p′) : The Case 1 (2004) (10)
Integrals of motion of the classical lattice sine-Gordon system (1994) (10)
A φ1,3-Filtration of the Virasoro Minimal Series M(p, p') with 1 < p'/p < 2 (2008) (9)
3-Manifolds and VOA Characters (2022) (9)
Principal $\widehat{\mathfrak{sl}_3}$ subspaces and quantum Toda Hamiltonian (2009) (9)
Quantum toroidal gl sub 1-algebra: Plane partitions: plane partitions (2012) (9)
The Integrals of Motion for the Deformed W-Algebra Wqt(sl_N^) (2007) (8)
Principal subspace for the bosonic vertex operator ϕ2m(z) and Jack polynomials (2006) (8)
Commutative quantum current operators, semi-infinite construction and functional models (1996) (8)
Jones optimality and hardware virtualization: a report on work in progress (2008) (8)
Regular Representation of Affine Kac-Moody Algebras (1996) (8)
Combinatorics of the b sl 2 Coinvariants : Dual Functional Realization and Recursion (2002) (7)
Truncation of functional relations in the $XXZ$ model. (2000) (7)
Deformation of Weyl Modules and Generalized Parking Functions (2003) (7)
Generating Series of the Poincaré Polynomials of Quasihomogeneous Hilbert Schemes (2012) (7)
CERTAIN TOPICS ON THE LIE ALGEBRA gl(λ) REPRESENTATION THEORY (1997) (7)
Stable cohomology of the algebra Wn and relations in the algebra L1 (1984) (6)
An evaluation homomorphism for quantum toroidal gl(n) algebras (2017) (6)
Generalized KDV flows and nilpotent subgroups of affine Kac-Moody groups (1993) (6)
Two-dimensional current algebras and affine fusion product (2006) (6)
Sets of rigged paths with Virasoro characters (2005) (6)
Spaces of coinvariants and fusion product II. Affine sl_2 character formulas in terms of Kostka polynomials (2002) (5)
Dual description of η-deformed OSP sigma models (2020) (5)
Integrable $\hat{\mathfrak{sl}_2}$-modules as infinite tensor products (2002) (5)
Bethe subalgebras of quantum affine gl(n) via shuffle algebras (2015) (5)
A Simple Proof of the Formula for the Betti Numbers of the Quasihomogeneous Hilbert Schemes (2013) (5)
A functional model for the tensor product of level 1 highest and level -1 lowest modules for the quantum affine algebra Uq(sT2) (2003) (5)
Equivalence between Chain Categories of Representations of Affine s l ( 2 ) and N = 2 Superconformal (1998) (5)
Combinatorics of vertex operators and deformed W-algebra of type D(2,1;α) (2021) (5)
Abelianization of the BGG resolution of representations of the Virasoro algebra (2011) (5)
GEOMETRICAL DESCRIPTION OF THE LOCAL INTEGRALS OF MOTION OF MAXWELL-BLOCH EQUATION (1995) (4)
The conformal field theory from the view of the cohomology theory of the Lie algebras (1990) (4)
Semi-infinite Weil complex and the Virasoro algebra (1991) (4)
PRINCIPLE SUBSPACE FOR BOSONIC VERTEX OPERATOR φ √ 2m (z) AND JACK POLYNOMIALS (2004) (4)
Kernel function and quantum algebras (表現論と組合せ論--RIMS研究集会報告集) (2010) (4)
Elliptic Sklyanin algebras. The case of points of finite order (1995) (4)
The coset theory as a Hamiltonian reduction of (2001) (4)
Regular representations of affine Kac-Moody algebras (1993) (4)
hep-th/9907171 ̂sℓ(2|1) AND ̂ D(2|1; α) AS VERTEX OPERATOR EXTENSIONS OF DUAL AFFINE sℓ(2) ALGEBRAS (1999) (4)
A combinatorial formula for affine Hall–Littlewood functions via a weighted Brion theorem (2015) (4)
Evaluation modules for quantum toroidal ${\mathfrak{gl}}_n$ algebras (2017) (4)
The $${(\mathfrak{gl}_{m},\mathfrak{gl}_{n})}$$(glm,gln) Duality in the Quantum Toroidal Setting (2018) (3)
The $(\mathfrak{gl}_m,\mathfrak{gl}_n$) duality in the quantum toroidal setting (2018) (3)
Differential operators on the moduli space of G-bundles on algebraic curve and Lie algebra cohomologies (1991) (3)
On bosonization of 2d conformal field theories (1994) (3)
Integrable Systems, Shuffle Algebras, and Bethe Equations (2016) (3)
Two Character Formulas for { {sl}}2 Spaces of Coinvariants (2004) (3)
On the Endomorphisms of Weyl Modules over Affine Kac–Moody Algebras at the Critical Level (2008) (3)
Coordinate ring of the quantum Grassmanian and intertwiners for the representations of Sklyanin algebras (1997) (3)
Quantized W-algebra of and Quantum Parafermions of (2000) (3)
Deformations of $$\mathcal {W}$$ algebras via quantum toroidal algebras (2020) (3)
Generalized Drinfeld realization of quantum superalgebras and $U_q(\hat {\frak osp}(1,2))$ (1999) (2)
Tableau Formulas for One-Row Macdonald Polynomials of Types C n and D n ? (2014) (2)
Correction to: Fermionic Formulas for Eigenfunctions of the Difference Toda Hamiltonian (2018) (2)
KERNEL FUNCTION AND QUANTUM ALGEBRAS (Representation Theory and Combinatorics) (2010) (2)
Combinatorics of the $\hat{sl_2}$ spaces of coinvariants II (1999) (2)
TWO CHARACTER FORMULAS FOR $\widehat{\mathfrak{sl}}_2$ SPACES OF COINVARIANTS (2002) (2)
Cohomology of the infinite-dimensional Lie algebra $L_1$ with nontrivial coefficients (1987) (2)
Homogeneous components in the moduli space of sheaves and Virasoro characters (2011) (2)
Shuffle algebra realization of quantum affine superalgebra Uv(Dˆ(2,1;θ)) (2021) (2)
Tutte decomposition for graphs, weighted graphs, and symmetric matrices. (1998) (1)
Products of Symbol Algebras That Ramify Only on a Nonsingular Plane Elliptic Curve (1992) (1)
Combinatorics of a statistical model constructed from the 2 × n square lattice (2017) (1)
Gelfand-Zetlin basis, Whittaker Vectors and a Bosonic Formula for the ${\mathfrak{sl}}_{n+1}$ Principal Subspace (2011) (1)
The conformal field theory from the view of the cohomology theory of the Lie algebras : plenary address, International Congress of Mathematicians, Kyoto, Japan, August, 1990 (1990) (1)
Interpretational overhead in system software (2011) (1)
Principle subspace for bosonic vertex operator $\phi_{\sqrt{2m}}(z)$ and Jack polynomials (2004) (1)
A $\phi_{1,3}$-filtration of the Virasoro minimal series M(p,p') with 1 (2006) (1)
Q A ] 1 8 A ug 2 01 7 INTEGRALS OF MOTION FROM QUANTUM TOROIDAL ALGEBRAS (0)
Functional equations in algebra (2017) (0)
2 1 A ug 2 00 2 SPACES OF COINVARIANTS AND FUSION PRODUCT II . ŝl 2 CHARACTER FORMULAS IN TERMS OF KOSTKA (2002) (0)
IDENTITIES FROM COMBINATIONS OF VIRASORO CHARACTERS (2008) (0)
Introduction to Lie algebra cohomology (1993) (0)
Gelfand-Zetlin basis, Whittaker vectors and a bosonic formula for the $\sln$ principal subspace (2009) (0)
A construction of level 1 irreducible modules for $U_q(\hat{sp}_4)$ using level 2 intertwiners for $U_q(\hat{sl}_2)$ (2002) (0)
Commutative vertex algebras and their degenerations (2014) (0)
Cohomology of nilpotent subalgebras of the algebra $$\widehat{sl_2 }$$ (1996) (0)
A ] 1 7 Ja n 19 99 Extended Vertex Operator Algebras and Monomial Bases (2008) (0)
REALIZATION OF THE RESTRICTED (2009) (0)
SEMI-INFINITE CONSTRUCTION AND FUNCTIONAL MODELS (0)
Tableau formula for Macdonald polynomial of type C_n and D_n with one row diagram (2014) (0)
Serge G. Vlăduţ (2004) (0)
Dedicated to Professor Heisuke Hironaka on the occasion of his seventy-seventh birthday (2008) (0)
Flat deformations of algebras and functional equations (2019) (0)
The Intergals of Motion for (2006) (0)
AS VERTEX OPERATOR EXTENSIONS OF DUAL AFFINE s l ( 2 ) ALGEBRAS (2022) (0)
Formally Efficient Program Instrumentation (2010) (0)
ec 2 00 8 YANGIANS AND COHOMOLOGY RINGS OF LAUMON SPACES (0)
Shuffle algebra realization of quantum affine superalgebra $U_{v}(\hat{\mathfrak{D}}(2,1;\theta))$ (2019) (0)
The Erwin Schrr Odinger International Institute for Mathematical Physics Modular Functor and Representation Theory of B Sl 2 at a Rational Level Modular Functor and Representation Theory of D Sl 2 at a Rational Level (2009) (0)
Drinfeld realization of quantum superalgebras and U q (̂(1,2)) (2000) (0)
The Intergals of Motion for the Deformed Virasoro Algebra March 18 , 2008 Dedicated to Professor Masaki Kashiwara on the occasion on the 60 th birthday (2008) (0)
S ep 2 00 2 SPACES OF COINVARIANTS AND FUSION PRODUCT I . FROM EQUIVALENCE THEOREM TO KOSTKA (2002) (0)
Deformation quantization with traces and vanishing of the wheels (2000) (0)
A CONSTRUCTION OF LEVEL 1 IRREDUCIBLE MODULES FOR Uq(ŝp4) USING LEVEL 2 INTERTWINERS FOR Uq(ŝl2) (2002) (0)
Shuffle algebra realization of quantum affine superalgebras with fermionic simple root system (2019) (0)
Mechanism for Fine-Grained Software Controlled Core Dumps (2017) (0)
The $\hat{sl}(2)+\hat{sl}(2)/\hat{sl}(2)$ Coset Theory as a Hamiltonian Reduction of $\hat{D}(2|1;\alpha)$ (2001) (0)
2 7 M ar 2 01 1 Yangians and cohomology rings of Laumon spaces (2011) (0)
New trends in quantum integrable systems : proceedings of the Infinite Analysis 09 : Kyoto, Japan, 27-31 July 2009 (2011) (0)
1 0 Fe b 20 18 PLANE PARTITIONS WITH A “ PIT ” : GENERATING FUNCTIONS AND REPRESENTATION THEORY (2021) (0)
OF THE ŝl 2 SPACES OF COINVARIANTS III (2001) (0)
O ct 2 00 2 SPACES OF COINVARIANTS AND FUSION PRODUCT II . ŝl 2 CHARACTER FORMULAS IN TERMS OF KOSTKA (2002) (0)
FROM EQUIVALENCE THEOREM TO KOSTKA (2002) (0)

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Boris Feigin is affiliated with the following schools: