Nolan Wallach

Q: What Schools Are Affiliated With Nolan Wallach

Nolan Wallach is affiliated with the following schools: University of California, Berkeley, Washington University in St. Louis, Rutgers University, University of California, San Diego

Nolan Wallach's AcademicInfluence.com Rankings

Nolan Wallach

Mathematics

#1384

World Rank

#2292

Historical Rank

#574

USA Rank

Measure Theory

#897

World Rank

#1173

Historical Rank

#333

USA Rank

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Mathematics

Why Is Nolan Wallach Influential?

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According to Wikipedia, Nolan Russell Wallach is a mathematician known for work in the representation theory of reductive algebraic groups. He is the author of the 2-volume treatise Real Reductive Groups. Education and career Wallach did his undergraduate studies at the University of Maryland, graduating in 1962. He earned his Ph.D. from Washington University in St. Louis in 1966, under the supervision of Jun-Ichi Hano.

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Nolan Wallach's Published Works

Number of citations in a given year to any of this author's works

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

Continuous Cohomology, Discrete Subgroups, and Representations of Reductive Groups (1999) (986)
Representations and Invariants of the Classical Groups (1998) (839)
Real reductive groups (1988) (606)
Real Reductive Groups II (1988) (516)
Symmetry, Representations, and Invariants (2009) (468)
Global entanglement in multiparticle systems (2001) (382)
Compact Homogeneous Riemannian Manifolds with Strictly Positive Curvature (1972) (301)
A Classification of Unitary Highest Weight Modules (1983) (271)
An infinite family of distinct 7-manifolds admitting positively curved Riemannian structures (1975) (269)
The analytic continuation of the discrete series. II (1979) (165)
Minimal immersions of spheres into spheres. (1969) (162)
Asymptotic expansions of generalized matrix entries of representations of real reductive groups (1983) (146)
On a classification of the gradient shrinking solitons (2007) (135)
Limit Formulas for Multiplicities in L 2 (Γ\G) (1978) (127)
Structure and unitary cocycle representations of loop groups and the group of diffeomorphisms of the circle. (1984) (122)
Projective modules over graded Lie algebras. I (1982) (122)
On the Selberg trace formula in the case of compact quotient (1976) (121)
On quaternionic discrete series representations, and their continuations. (1996) (113)
All maximally entangled four-qubit states (2010) (110)
Composition series and intertwining operators for the spherical principal series (1972) (108)
Projective unitary positive-energy representations of Diff (S1) (1985) (106)
Global hypoellipticity and Liouville numbers (1972) (93)
Szegö kernels associated with discrete series (1976) (82)
Invariant differential operators on a reductive Lie algebra and Weyl group representations (1993) (77)
Whittaker vectors and conical vectors (1980) (75)
Gelfand-Zeitlin Theory from the Perspective of Classical Mechanics. II (2004) (73)
Classification of multipartite entanglement of all finite dimensionality. (2013) (72)
Lie Algebra Cohomology and Holomorphic Continuation of Generalized Jacquet Integrals (1988) (69)
Classical and quantum-mechanical systems of Toda lattice type. I (1982) (65)
Notes on homological algebra and representations of Lie algebras (1980) (64)
On the unitarizability of derived functor modules (1984) (57)
A Distinguished Family of Unitary Representations for the Exceptional Groups of Real Rank = 4 (1994) (56)
Intertwining operators for real reductive groups (1990) (54)
Symplectic geometry and Fourier analysis (1977) (48)
Highest weight modules over graded Lie algebras: resolutions, filtrations and character formulas (1983) (47)
Cyclic vectors and irreducibility for principal series representations. II (1971) (45)
Limit Formulas for Multiplicities in L 2 (Γ\G) II. The Tempered Spectrum (1979) (41)
Representations of compact groups and minimal immersions into spheres. (1970) (41)
Restriction of small discrete series represen-tations to symmetric subgroups (2000) (39)
An Unentangled Gleason's Theorem (2000) (39)
On the Enright-Varadarajan modules : a construction of the discrete series (1976) (38)
Generalized Whittaker vectors for holomorphic and quaternionic representations (2003) (37)
THE ANALYTIC CONTINUATION OF THE DISCRETE SERIES (2010) (36)
Transformations among Pure Multipartite Entangled States via Local Operations are Almost Never Possible (2017) (36)
REVISITING HOMOGENEOUS SPACES WITH POSITIVE CURVATURE (2015) (36)
THE ANALYTIC CONTINUATION OF THE DISCRETE SERIES (2010) (36)
Characters of irreducible representations of the Lie algebra of vector fields on the circle (1983) (35)
Higher-order Sugawara operators for affine Lie algebras (1989) (34)
Globally hypoelliptic vector fields (1973) (34)
Classical and quantum mechanical systems of Toda-lattice type (1984) (33)
Necessary and sufficient conditions for local manipulation of multipartite pure quantum states (2011) (33)
Automorphic forms constructed from Whittaker vectors (1989) (32)
Unitary derived functor modules with small spectrum (1985) (31)
Characters of irreducible representations of the virasoro algebra (1984) (31)
The resolvent of the Laplacian on locally symmetric spaces (1992) (30)
NICE PARABOLIC SUBALGEBRAS OF REDUCTIVE LIE ALGEBRAS (2004) (30)
Remarks on global hypoellipticity (1973) (29)
An asymptotic formula of Gelfand and Gangolli for the spectrum of $G\backslash G$ (1976) (29)
Finite- and infinite-dimensional representation of linear semisimple groups (1973) (28)
The Hilbert Series of Measures of Entanglement for 4 Qubits (2005) (28)
Geometric Invariant Theory: Over the Real and Complex Numbers (2017) (28)
Kuznetsov formulas for real rank one groups (1990) (27)
ON HARISH-CHANDRA'S GENERALIZED C-FUNCTIONS. (1975) (27)
MINIMAL IMMERSIONS OF SYMMETRIC SPACES INTO SPHERES (2014) (24)
On the Hilbert polynomials and Hilbert series of homogeneous projective varieties (2007) (24)
Almost all multipartite qubit quantum states have trivial stabilizer (2016) (23)
On the nullcone of representations of reductive groups (2006) (23)
Classical and quantum mechanical systems of Toda-lattice type (1986) (21)
Entanglement of Subspaces and Error Correcting Codes (2007) (21)
The fundamental series of representations of a real semisimple Lie algebra (1978) (20)
On Matsushima's formula for the Betti numbers of a locally symmetric space (1975) (20)
On 4-dimensional gradient shrinking solitons (2007) (20)
Invariants for Multiple Qubits: The Case of 3 Qubits (2002) (20)
Induced representations of Lie algebras and a theorem of Borel-Weil. (1969) (20)
Introductory lectures on automorphic forms (2001) (19)
Qsym over Sym is free (2003) (18)
A combinatorial problem associated with nonograms (2006) (16)
Square integrable automorphic forms and cohomology of arithmetic quotients of SU(p, q) (1984) (16)
Algebraic Groups and Homogeneous Spaces (2009) (16)
Automorphism groups of bounded domains in Banach spaces (1972) (16)
Holomorphic continuation of generalized Jacquet integrals for degenerate principal series (2006) (15)
Continuous and differentiable cohomology for locally compact totally disconnected groups (2000) (15)
Completeness of Poincaré Series for Automorphic Forms Associated to the Integrable Discrete Series (1983) (15)
Quantum Computing and Entanglement for Mathematicians (2008) (15)
Local distinguishability of generic unentangled orthonormal bases (2015) (15)
On Maximal Subsystems of Root Systems (1968) (15)
On Some $q$ -Analogs of a Theorem of Kostant-Rallis (2000) (14)
Induced representations of Lie algebras. II (1969) (14)
The restriction of admissible modules to parabolic subalgebras (1982) (14)
Resolvent and lattice points on symmetric spaces of strictly negative curvature (1999) (14)
Properties and examples of FCR-algebras (2001) (13)
Harmonic Analysis, Group Representations, Automorphic Forms and Invariant Theory: In Honor of Roger E Howe (2007) (13)
Correction and addition to Szegö kernels associated with discrete series (1980) (13)
Representations of Reductive Groups (1980) (13)
Ricci flow and curvature on the variety of flags on the two dimensional projective space over the complexes, quaternions and octonions (2012) (13)
Kronecker coefficients via Symmetric Functions and Constant Term Identities (2012) (12)
On a theorem of Milnor and Thom (1996) (12)
On the irreducibility and inequivalence of unitary representations of gauge groups (1987) (12)
Embeddings of unitary highest weight representations and generalized Dirac operators (1997) (12)
On the unitarizability of representations with highest weights (1975) (11)
Invariants, Kronecker products, and combinatorics of some remarkable Diophantine systems (2008) (11)
A new plethystic symmetric function operator and the rational compositional shuffle conjecture at t = 1/q (2015) (11)
Harmonic differential forms for pseudo-reflection groups I. Semi-invariants (2020) (11)
Curvature forms for 2-manifolds (1970) (11)
Representation Theory and Complex Analysis (2008) (11)
A class of non-standard modules for affine Lie algebras (1987) (10)
The asymptotic behavior of holomorphic representations (1984) (10)
The non-degeneracy of the bilinear form of m-Quasi-Invariants (2006) (9)
r-Qsym is free over Sym (2007) (8)
A Pieri rule for Hermitian symmetric pairs II (2004) (8)
New Developments in Lie Theory and Their Applications (1992) (8)
Polarizations and Nullcone of Representations of Reductive Groups (2010) (8)
Hilbert series of invariants, constant terms and Kostka-Foulkes polynomials (2009) (8)
Homogeneous positively pinched Riemannian manifolds (1970) (8)
Dimensions of spaces of generalized spherical functions (1996) (8)
Some implications of a conjecture of Zabrocki to the action of $S_{n}$ on polynomial differential forms (2019) (8)
Structure and unitary cocycle representations of loop groups and the group of diffeomorphisms of the circle (1984) (8)
Hereditary properties of direct summands of algebras (1999) (7)
Limit multiplicities in L2(Γ∖G) (1990) (7)
Classical Invariant Theory and the Virasoro Algebra (1985) (7)
TRANSFER OF UNITARY REPRESENTATIONS (2004) (6)
On symmetric SL-invariant polynomials in four qubits (2012) (6)
Application of the higher osculating spaces to the spherical principal series (1971) (6)
Harmonic differential forms for pseudo-reflection groups II. Bi-degree bounds (2021) (6)
On the separation property of orbits in representation spaces (2002) (5)
Shorter Notes: Curvature Forms for 2-Manifolds (1970) (5)
Some new Applications of Orbit Harmonics by (2004) (4)
Bessel models for general admissible induced representations: the compact stabilizer case (2010) (4)
The restriction of Whittaker modules to certain parabolic subalgebras (1981) (4)
Action of the conformal group on steady state solutions to Maxwell’s equations and background radiation (2011) (3)
The Hilbert ball and bi-ball are holomorphically inequivalent (1971) (3)
Harmonics for Deformed Steenrod Operators (2008) (3)
A quantum polylog algorithm for non-normal maximal cyclic hidden subgroups in the affine group of a finite field (2013) (3)
PFAFFIANS AND STRATEGIES FOR INTEGER CHOICE GAMES (2007) (3)
On the algebraic set of singular elements in a complex simple Lie algebra (2010) (3)
Three new examples of compact manifolds admitting Riemannian structures of positive curvature (1972) (3)
On the Gelfand–Kirillov dimension of a discrete series representation (2015) (2)
On a Theorem of Ranee Brylinski (2009) (2)
Representations of SL 2 and the distribution of points in ℙ n (2002) (2)
Corrigendum: Necessary and sufficient conditions for local manipulation of multipartite pure quantum states (2011 New J. Phys. 13 073013) (2019) (2)
Combinatorial aspects of the Baker-Akhiezer functions for S2 (2004) (2)
Classification of multipartite entanglement in all dimensions (2018) (2)
Fréchet completions of moderate growth old and (somewhat) new results (2014) (2)
Applications of representation theory to harmonic analysis of Lie groups (and vice versa) (2008) (2)
Algebras and Representations (2009) (2)
On the Whittaker Plancherel Theorem for Real Reductive Groups (2017) (2)
Pfaffians of Toeplitz payoff matrices (2019) (2)
Classes of unitarizable derived functor modules. (1983) (2)
Principal orbit type theorems for reductive algebraic group actions and the Kempf--Ness Theorem (2018) (2)
A class of gradings of simple Lie algebras (2006) (1)
Positive-Energy Representations of the Group of Diffeomorphisms of the Circle (1985) (1)
The dependence on parameters of the inverse functor to the 𝐾-finite functor (2020) (1)
Some new Applications of (2004) (1)
A Variety of Solutions to the Yang-Baxter Equation (1999) (1)
An Analogue of the Kostant–Rallis Multiplicity Theorem for θ-Group Harmonics (2017) (1)
On the Whittaker Plancherel Theorem (2017) (1)
Structure of Classical Groups (2009) (1)
Representations on Spaces of Regular Functions (2009) (0)
AUTOMORPHISM GROUPS OF BOUNDED DOMAINS (2010) (0)
Dependence on parameters of CW globalizations of families of Harish-Chandra modules and the meromorphic continuation of $C^{\infty}$ Eisenstein series. (2019) (0)
Some New Methods in the Theory of m-Quasi-Invariants (2005) (0)
Tensor Representations of O(V) and Sp(V) (2009) (0)
The Affine Theory (2017) (0)
Hilbert Series of Invariants, Constant terms (2007) (0)
Notation and preliminaries (2000) (0)
Compact minimal submanif olds of a sphere with positive Ricci curvature (2006) (0)
Highest-Weight Theory (2009) (0)
via Symmetric Functions and Constant Term identities (2010) (0)
Representation Theory and Automorphic Forms (2010) (0)
Appendix G Group Representations and the Platonic Solids (2009) (0)
Lie Groups and Algebraic Groups (2009) (0)
The spherical Whittaker Inversion Theorem and the quantum non-periodic Toda Lattice (2023) (0)
Classical Invariant Theory (2009) (0)
Contemporary Mathematics An Unentangled Gleason ’ s Theorem (2002) (0)
Shor's algorithm without partial fractions (2012) (0)
M-series and Kloosterman–Selberg zeta functions for ℝ-rank one groups (2014) (0)
Cohomology with coefficients in Π_ (2000) (0)
Erratum: Nice parabolic subalgebras of reductive Lie algebras (2005) (0)
qu an tph ] 1 4 Ju l 2 01 0 All Maximally Entangled Four Qubits States (2010) (0)
Bessel models for general admissible induced representations: the compact stabilizer case (2011) (0)
The computation of certain cohomology groups (2000) (0)
Non-cocompact -arithmetic subgroups (2000) (0)
On a question related to a basic convergence theorem of Harish-Chandra (2022) (0)
Cohomology with respect to an induced representation (2000) (0)
THE RESTRICTION OF ADMISSIBLE MODULES (2010) (0)
O ct 2 00 7 Entanglement of Subspaces and Error Correcting Codes (2018) (0)
Tensor Representations of GL(V) (2009) (0)
Continuous cohomology and differentiable cohomology (2000) (0)
An evolution in six stages based on triality: A mathematical memoir (2021) (0)
An analogue of the Kostant-Rallis multiplicity theorem for $\theta$-group harmonics (2016) (0)
Some applications of group representations (1990) (0)
Cohomology of discrete subgroups and Lie algebra cohomology (2000) (0)
Differentiable cohomology for products of real Lie groups and T.D. groups (2000) (0)
Appendix F Decomposition of Tensor Spaces for O ( V ) and Sp ( V ) (2009) (0)
Cohomology with coefficients in Π_{∞}(): The -adic case (2000) (0)
Cohomology of discrete cocompact subgroups (2000) (0)
The construction of certain unitary representations and the computation of the corresponding cohomology groups (2000) (0)
Weight Theory in Geometric Invariant Theory (2017) (0)
Unentangled measurements and frame functions (2017) (0)
Relative Lie algebra cohomology (2000) (0)
Harmonics for deformed Steenrod operators (Extended Abstract) (2010) (0)
Stability theorems for multiplicities in graded $S_n$-modules (2021) (0)
Armand Borel: A Reminiscence (2004) (0)
Scalar product, Laplacian and Casimir element (2000) (0)
The Langlands classification and uniformly bounded representations (2000) (0)
On Neeman's gradient flows (2016) (0)
Classical and Geometric Invariant Theory for Products of Classical Groups (2017) (0)
Polarization and nullcone of reductive groups (2010) (0)
Local manipulation of multipartite entanglement (2018) (0)

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What Schools Are Affiliated With Nolan Wallach?

Nolan Wallach is affiliated with the following schools: