Igor Frenkel

Q: What Schools Are Affiliated With Igor Frenkel

Igor Frenkel is affiliated with the following schools: Saint Petersburg State University, Moscow State University, Yale University, University of California, Santa Barbara, Stony Brook University, University of California, Irvine, Rutgers University, University of Chicago

Igor Frenkel's AcademicInfluence.com Rankings

Igor Frenkel

Mathematics

#246

World Rank

#536

Historical Rank

#118

USA Rank

Algebra

#14

World Rank

#28

Historical Rank

USA Rank

Measure Theory

#2399

World Rank

#2869

Historical Rank

#681

USA Rank

mathematics Degrees

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Mathematics

Igor Frenkel's Degrees

PhD Mathematics Moscow State University

Why Is Igor Frenkel Influential?

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According to Wikipedia, Igor Borisovich Frenkel is a Russian-American mathematician at Yale University working in representation theory and mathematical physics. Frenkel emigrated to the United States in 1979. He received his PhD from Yale University in 1980 with a dissertation on the "Orbital Theory for Affine Lie Algebras". He held positions at the IAS and MSRI, and a tenured professorship at Rutgers University, before taking his current job of tenured professor at Yale University. He was elected to the National Academy of Sciences in 2018. He is also a Fellow of the American Academy of Arts and Sciences.

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Igor Frenkel'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

Vertex Operator Algebras and the Monster (2011) (1099)
On Axiomatic Approaches to Vertex Operator Algebras and Modules (1993) (1050)
Vertex operator algebras associated to representations of affine and Virasoro Algebras (1992) (875)
Basic representations of affine Lie algebras and dual resonance models (1980) (820)
A Categorification of the Jones Polynomial (2008) (805)
Quantum affine algebras and holonomic difference equations (1992) (614)
Lectures on Representation Theory and Knizhnik-Zamolodchikov Equations (1998) (294)
Four‐dimensional topological quantum field theory, Hopf categories, and the canonical bases (1994) (290)
A natural representation of the Fischer-Griess Monster with the modular function J as character. (1984) (274)
Vertex representations of quantum affine algebras. (1988) (260)
Two constructions of affine Lie algebra representations and boson-fermion correspondence in quantum field theory (1981) (212)
A hyperbolic Kac-Moody algebra and the theory of Siegel modular forms of genus 2 (1983) (191)
Elliptic solutions of the Yang-Baxter equation and modular hypergeometric functions (1997) (186)
Spinor Construction of Vertex Operator Algebras, Triality, and E (1991) (184)
Semi-infinite cohomology and string theory. (1986) (177)
A categorification of the Temperley-Lieb algebra and Schur quotients of $ U({\frak sl}_2) $ via projective and Zuckerman functors (1999) (142)
Classical affine algebras (1985) (138)
Isomorphism of two realizations of quantum affine algebra $$U_q (\widehat{\mathfrak{g}\mathfrak{l}{\text{(}}n{\text{)}}})$$ (1993) (113)
Vertex operator calculus (1987) (109)
A categorification of finite-dimensional irreducible representations of quantum sl(2) and their tensor products (2005) (102)
A moonshine module for the Monster (1985) (102)
Quantum Vertex Representations via Finite Groups¶and the McKay Correspondence (1999) (97)
Orbital theory for affine Lie algebras (1984) (92)
Canonical bases in tensor products and graphical calculus for $U_q(\mathfrak{sl}_2)$ (1997) (89)
Central extensions of current groups in two dimensions (1993) (88)
Representations of affine lie algebras, hecke modular forms and korteweg—De vries type equations (1982) (87)
A Categorification of the Temperley-Lieb Algebra and Schur Quotients of U(sl2) via Projective and (2000) (85)
Rademacher sums, moonshine and gravity (2009) (84)
Spherical functions on affine Lie groups (1994) (78)
Spinor representations of affine Lie algebras. (1980) (78)
Kazhdan-Lusztig polynomials and canonical basis (1997) (73)
A categorification of finite-dimensional irreducible representations of quantum $${\mathfrak{sl}_2}$$ and their tensor products (2007) (60)
Positive representations of split real quantum groups and future perspectives (2011) (55)
Categorifying fractional Euler characteristics, Jones–Wenzl projectors and 3j-symbols (2012) (55)
Split quaternionic analysis and separation of the series for SL ( 2 , R ) and SL ( 2 , C ) / SL ( 2 (2010) (51)
Spinor construction of vertex operator algebras (1991) (46)
Virasoro Algebra and Wreath Product Convolution (2000) (41)
Affine Lie algebras and tame quivers (2000) (41)
Categorifying fractional Euler characteristics, Jones-Wenzl projector and $3j$-symbols with applications to Exts of Harish-Chandra bimodules (2010) (38)
Level 1 perfect crystals and path realizations of basic representations at q = 0 (2005) (33)
Complex ADHM equations and sheaves on P 3 (2008) (32)
Quantum Teichmüller space from the quantum plane (2010) (31)
Bases of Representations of Type A Affine Lie Algebras via Quiver Varieties and Statistical Mechanics (2002) (31)
Simplex equations and their solutions (1991) (29)
Modified regular representations of affine and Virasoro algebras, VOA structure and semi-infinite cohomology (2004) (28)
Four dimensional realization of two dimensional current groups (1996) (27)
Vertex algebras associated to modified regular representations of the Virasoro algebra (2012) (23)
Annihilating ideals and tilting functors (1998) (22)
Gelfand–Tsetlin algebras and cohomology rings of Laumon spaces (2008) (22)
Spinor and Oscillator Representations of Quantum Groups (1994) (21)
Quaternionic analysis, representation theory and physics II (2007) (21)
A Categorification of the Boson–Fermion Correspondence via Representation Theory of sl(∞) (2014) (19)
Complex counterpart of Chern-Simons-Witten theory and holomorphic linking (2005) (18)
Twisted vertex representations via spin groups and the McKay correspondence (2000) (17)
Representations of Kac-Moody Algebras and Dual Resonance Models (2021) (17)
Quantum Instantons with Classical Moduli Spaces (2002) (14)
Trigonometric Solutions of the Yang-Baxter Equation, Nets, and Hypergeometric Functions (1995) (14)
Quantum Group as Semi-infinite Cohomology (2008) (13)
Homological realization of Nakajima varieties and Weyl group actions (2003) (13)
Canonical Basis and Macdonald Polynomials (1998) (12)
Representations of Hyperbolic Kac-Moody Algebras (1993) (12)
Current developments and future perspectives (1998) (10)
Canonical Basis and Homology of Local Systems (1997) (9)
Quaternionic Analysis and the Schrödinger Model for the Minimal Representation of O(3,3) (2011) (8)
An introduction to the Monster (1986) (7)
Quiver varieties, affine Lie algebras, algebras of BPS states, and semicanonical basis (2002) (7)
Chapter 0: Introduction (1991) (7)
Complex ADHM equations, sheaves on P^3 and quantum instantons (2004) (6)
Anti De Sitter Deformation of Quaternionic Analysis and the Second Order Pole (2014) (5)
Vertex operator algebras associated to modified regular representations of the Virasoro algebra (2010) (4)
Sketch of a Program for Automorphic Functions from Universal Teichmüller Theory to Capture Monstrous Moonshine (2022) (3)
Kazhdan-Lusztig tensoring and Harish-Chandra categories (1997) (3)
Representations of affine Lie algebras and soliton equations (1985) (2)
On the continuous series for affine sl(2,R) (2012) (2)
Sketch of a Program for Universal Automorphic Functions to Capture Monstrous Moonshine (2020) (1)
Quantum group GLq(2) and quantum Laplace operator via semi-infinite cohomology (2011) (1)
Representations of finite-dimensional and affine Lie algebras (1998) (1)
On The Continuous Series for $${{\widehat{sl(2,{\mathbb{R}})}}}$$sl(2,R)^ (2014) (1)
Introduction from the book "Vertex operator algebras and the Monster" (1991) (1)
ec 2 00 8 Quantum Group as Semi-infinite Cohomology (2008) (0)
Local systems and configuration spaces (1998) (0)
Knizhnik-Zamolodchikov equations (1998) (0)
Chapter 6: Spinor Construction of a Vertex Operator Para-algebra for ⁽¹⁾₄ (1991) (0)
Chapter 2: Affine Algebras and Representations (1991) (0)
A natural representation oftheFischer-Griess Monster withthemodular function Jascharacter (vertex operators/finite simple groupFl/Monstrous Moonshine/affine Liealgebras/basic modules) (1984) (0)
Chapter 1: Summary (1991) (0)
Solutions of the quantum Knizhnik-Zamolodchikov equations for ₂ (1998) (0)
Q A ] 2 7 Ju l 2 00 0 TWISTED VERTEX REPRESENTATIONS VIA SPIN GROUPS AND THE MCKAY (2021) (0)
Chapter 5: Spinor Construction of Triality for ⁽¹⁾₄ (1991) (0)
On the work of Igor Frenkel Introduction by (2012) (0)
Quantum affine algebras (1998) (0)
Solutions of the Knizhnik-Zamolodchikov equations (1998) (0)
Chapter 8: Spinor Construction of Vertex Operator Algebras for ⁽¹⁾₈ (1991) (0)
Quantum Knizhnik-Zamolodchikov equations (1998) (0)
Monodromy of Knizhnik-Zamolodchikov equations (1998) (0)
Twisted vertex operators and McKay correspondence (2000) (0)
HOW VERTEX ALGEBRAS ARE ALMOST ALGEBRAS: ON A THEOREM OF BORCHERDS (2007) (0)
Three dimensional construction of the Virasoro-Bott group (2021) (0)
Connection matrices for the quantum Knizhnik-Zamolod- chikov equations and elliptic functions (1998) (0)
n-Regular functions in quaternionic analysis (2020) (0)
Chapter 7: Spinor Construction of ₈ (1991) (0)
1 2 Ju n 20 00 Virasoro algebra and wreath product convolution (2000) (0)
An $Esb 8$-approach to $Fsb 1$ (1985) (0)
A Categorification of the Boson–Fermion Correspondence via Representation Theory of sl(∞) (2015) (0)
Chapter 3: Spinor Construction of Vertex Operator Superalgebras (1991) (0)
Special Functions in Minimal Representations Toshiyuki Kobayashi (2013) (0)
Chapter 4: Spinor Construction of the Chevalley Algebra and Triality for ₄ (1991) (0)
A CATEGORIFICATION OF THE JONES POLYNOMIAL MIKHAIL KHOVANOV To my teacher (1999) (0)

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What Schools Are Affiliated With Igor Frenkel?

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Igor Frenkel's Academic­Influence.com Rankings

Igor Frenkel's Degrees

Why Is Igor Frenkel Influential?

Igor Frenkel's Published Works

Published Works

Other Resources About Igor Frenkel

What Schools Are Affiliated With Igor Frenkel?

Igor Frenkel's AcademicInfluence.com Rankings