I. Frenkel

发表

Vertex Operator Algebras and the Monster

J. Lepowsky, A. Meurman, I. Frenkel, 2011 .

Canonical Basis and Homology of Local Systems

A. Kirillov, A. Varchenko, I. Frenkel, 1997, q-alg/9703007.

Modified regular representations of affine and Virasoro algebras, VOA structure and semi-infinite cohomology

I. Frenkel, K. Styrkas, 2004, math/0409117.

REGULAR REPRESENTATIONS , VERTEX ALGEBRAS AND SEMI-INFINITE COHOMOLOGY 3 To transform the dual module V̂

I. Frenkel, K. Styrkas, 2022 .

Level 1 perfect crystals and path realizations of basic representations at q = 0

Seok-Jin Kang, Hyeonmi Lee, I. Frenkel, 2005, math/0507114.

Basic representations of affine Lie algebras and dual resonance models

V. Kac, I. Frenkel, 1980 .

A categorification of finite-dimensional irreducible representations of quantum sl(2) and their tensor products

C. Stroppel, M. Khovanov, I. Frenkel, 2005, math/0511467.

Quaternionic analysis, representation theory and physics II

Igor Frenkel, Matvei Libine, I. Frenkel, 2007, Advances in Theoretical and Mathematical Physics.

R T ] 2 5 M ay 2 00 8 Quaternionic Analysis , Representation Theory and Physics

I. Frenkel, M. Libine, 2008 .

A hyperbolic Kac-Moody algebra and the theory of Siegel modular forms of genus 2

I. Frenkel, A. Feingold, 1983 .

Lectures on Representation Theory and Knizhnik-Zamolodchikov Equations

P. Etingof, A. Kirillov, I. Frenkel, 1998 .

Four‐dimensional topological quantum field theory, Hopf categories, and the canonical bases

L. Crane, I. Frenkel, 1994, hep-th/9405183.

Classical affine algebras

I. Frenkel, A. Feingold, 1985 .

Quantum Group as Semi-infinite Cohomology

I. Frenkel, A. Zeitlin, 2008, 0812.1620.

ec 2 00 8 Quantum Group as Semi-infinite Cohomology

I. Frenkel, A. Zeitlin, 2008 .

Quantum Instantons with Classical Moduli Spaces

I. Frenkel, M. Jardim, 2002, math/0205118.

Isomorphism of two realizations of quantum affine algebra $$U_q (\widehat{\mathfrak{g}\mathfrak{l}{\text{(}}n{\text{)}}})$$

Jintai Ding, I. Frenkel, J. Ding, 1993 .

Quiver varieties, affine Lie algebras, algebras of BPS states, and semicanonical basis

I. Frenkel, M. Vybornov, A. Malkin, 2002, math-ph/0206012.

Semi-infinite cohomology and string theory.

I. Frenkel, G. Zuckerman, H. Garland, 1986, Proceedings of the National Academy of Sciences of the United States of America.

Spherical functions on affine Lie groups

P. Etingof, A. Kirillov, I. Frenkel, 1994, hep-th/9407047.

On Axiomatic Approaches to Vertex Operator Algebras and Modules

James Lepowsky, Yi-Zhi Huang, Igor B. Frenkel, 1993 .

Representations of affine lie algebras, hecke modular forms and korteweg—De vries type equations

I. Frenkel, 1982 .

Vertex operator algebras associated to representations of affine and Virasoro Algebras

I. Frenkel, Yongchang Zhu, 1992 .

Twisted vertex representations via spin groups and the McKay correspondence

N. Jing, I. Frenkel, Weiqiang Wang, 2000, math/0007159.

Representations of Kac-Moody Algebras and Dual Resonance Models

I. Frenkel, 2021 .

On the work of Igor Frenkel Introduction by

I. Frenkel, 2012 .

Twisted vertex representations via spin groups and the McKay correspondence

N. Jing, I. Frenkel, Weiqiang Wang, 2000, math/0007159.

A moonshine module for the Monster

J. Lepowsky, A. Meurman, I. Frenkel, 1985 .

Two constructions of affine Lie algebra representations and boson-fermion correspondence in quantum field theory

I. Frenkel, 1981 .

Spinor representations of affine Lie algebras.

I. Frenkel, Igor B. Frenkel, 1980, Proceedings of the National Academy of Sciences of the United States of America.

Spinor Construction of Vertex Operator Algebras, Triality, and E

Igor B. Frenkel, I. Frenkel, Alex J. Feingold, 1991 .

Quantum Vertex Representations via Finite Groups¶and the McKay Correspondence

N. Jing, I. Frenkel, Weiqiang Wang, 1999, 0909.1730.

Spinor construction of vertex operator algebras

Igor B. Frenkel, I. Frenkel, Alex J. Feingold, 1991 .

Quantum affine algebras and holonomic difference equations

N. Reshetikhin, I. Frenkel, 1992 .

Split quaternionic analysis and separation of the series for SL ( 2 , R ) and SL ( 2 , C ) / SL ( 2

I. Frenkel, M. Libine, 2010, 1009.2532.

Positive representations of split real quantum groups and future perspectives

I. Frenkel, I. Ip, 2011, 1111.1033.

A natural representation of the Fischer-Griess Monster with the modular function J as character.

J. Lepowsky, A. Meurman, I. Frenkel, 1984, Proceedings of the National Academy of Sciences of the United States of America.

Knizhnik-Zamolodchikov equations

P. Etingof, A. Kirillov, I. Frenkel, 1998 .

Orbital theory for affine Lie algebras

I. Frenkel, 1984 .

A Categorification of the Boson–Fermion Correspondence via Representation Theory of sl(∞)

V. Serganova, I. Frenkel, I. Penkov, 2015, Communications in Mathematical Physics.

Three dimensional construction of the Virasoro-Bott group

Igor B. Frenkel, Hyun Kyu Kim, I. Frenkel, 2021, 2107.11693.

Four dimensional realization of two dimensional current groups

B. Khesin, I. Frenkel, 1996 .

Central extensions of current groups in two dimensions

P. Etingof, I. Frenkel, 1993, hep-th/9303047.

Vertex operator calculus

J. Lepowsky, A. Meurman, I. Frenkel, 1987 .

Vertex algebras associated to modified regular representations of the Virasoro algebra

I. Frenkel, Minxian Zhu, 2012 .

Vertex representations of quantum affine algebras.

N. Jing, I. Frenkel, 1988, Proceedings of the National Academy of Sciences of the United States of America.

A Categorification of the Temperley-Lieb Algebra and Schur Quotients of U(sl2) via Projective and

M. Khovanov, I. Frenkel, Joseph N. Bernstein, 2000 .

Kazhdan-Lusztig polynomials and canonical basis

M. Khovanov, A. Kirillov, I. Frenkel, 1997, q-alg/9709042.

Canonical Basis and Macdonald Polynomials

N. Jing, J. Beck, I. Frenkel, 1998, math/9806151.

Spinor and Oscillator Representations of Quantum Groups

Jintai Ding, I. Frenkel, 1994 .

Vertex operator algebras associated to modified regular representations of the Virasoro algebra

I. Frenkel, Minxian Zhu, 2010, 1012.5443.

A categorification of finite-dimensional irreducible representations of quantum $${\mathfrak{sl}_2}$$ and their tensor products

C. Stroppel, M. Khovanov, I. Frenkel, 2007 .

A categorification of finite-dimensional irreducible representations of quantum sl(2) and their tensor products

C. Stroppel, M. Khovanov, I. Frenkel, 2005, math/0511467.

Complex ADHM equations and sheaves on P 3

I. Frenkel, M. Jardim, 2008 .

Complex ADHM equations, sheaves on P^3 and quantum instantons

I. Frenkel, M. Jardim, 2004, math/0408027.

Affine Lie algebras and tame quivers

I. Frenkel, M. Vybornov, A. Malkin, 2000, math/0005119.

A Categorification of the Jones Polynomial

Igor Frenkel, I. Frenkel, 2008 .

Complex counterpart of Chern-Simons-Witten theory and holomorphic linking

I. Frenkel, A. Todorov, 2005, math/0502169.

Virasoro Algebra and Wreath Product Convolution

I. Frenkel, Weiqiang Wang, 2000, math/0006087.

Categorifying fractional Euler characteristics, Jones–Wenzl projectors and 3j-symbols

C. Stroppel, I. Frenkel, Joshua Sussan, 2012 .

A categorification of the Temperley-Lieb algebra and Schur quotients of $ U({\frak sl}_2) $ via projective and Zuckerman functors

M. Khovanov, I. Frenkel, Joseph N. Bernstein, 1999, math/0002087.

Homological realization of Nakajima varieties and Weyl group actions

O. Schiffmann, M. Khovanov, I. Frenkel, 2003, Compositio Mathematica.

Categorifying fractional Euler characteristics, Jones-Wenzl projector and $3j$-symbols with applications to Exts of Harish-Chandra bimodules

C. Stroppel, I. Frenkel, Joshua Sussan, 2010, 1007.4680.

Annihilating ideals and tilting functors

I. Frenkel, F. Malikov, 1998, math/9801065.

Quantum Teichmüller space from the quantum plane

Hyun Kyu Kim, I. Frenkel, 2010, 1006.3895.

Representations of Hyperbolic Kac-Moody Algebras

I. Frenkel, John F. X. Ries, A. Feingold, 1993 .

Elliptic solutions of the Yang-Baxter equation and modular hypergeometric functions

Vladimir Turaev, Igor B. Frenkel, V. Turaev, 1997 .

On The Continuous Series for $${{\widehat{sl(2,{\mathbb{R}})}}}$$sl(2,R)^

I. Frenkel, A. Zeitlin, 2014 .

On the continuous series for affine sl(2,R)

I. Frenkel, A. Zeitlin, 2012, 1210.2135.

Sketch of a Program for Automorphic Functions from Universal Teichmüller Theory to Capture Monstrous Moonshine

R. Penner, I. Frenkel, 2022, Communications in Mathematical Physics.

Sketch of a Program for Universal Automorphic Functions to Capture Monstrous Moonshine

R. Penner, I. Frenkel, 2020, 2012.14220.

Rademacher sums, moonshine and gravity

I. Frenkel, J. Duncan, 2009, 0907.4529.

Quantum Vertex Representations via Finite Groups¶and the McKay Correspondence

N. Jing, I. Frenkel, Weiqiang Wang, 1999, 0909.1730.

1 2 Ju n 20 00 Virasoro algebra and wreath product convolution

I. Frenkel, Weiqiang Wang, 2000 .

Level 1 perfect crystals and path realizations of basic representations at q = 0

Seok-Jin Kang, Hyeonmi Lee, I. Frenkel, 2005, math/0507114.

Gelfand–Tsetlin algebras and cohomology rings of Laumon spaces

I. Frenkel, B. Feigin, M. Finkelberg, 2008, 0806.0072.

Special Functions in Minimal Representations Toshiyuki Kobayashi

Toshiyuki Kobayashi, I. Frenkel, 2013 .

Canonical bases in tensor products and graphical calculus for $U_q(\mathfrak{sl}_2)$

M. Khovanov, I. Frenkel, 1997 .

Quantum group GLq(2) and quantum Laplace operator via semi-infinite cohomology

I. Frenkel, A. Zeitlin, 2011, 1110.1696.

A Categorification of the Boson–Fermion Correspondence via Representation Theory of sl(∞)

V. Serganova, I. Frenkel, I. Penkov, 2014, 1405.7553.

Simplex equations and their solutions

G. Moore, I. Frenkel, 1991 .

Trigonometric Solutions of the Yang-Baxter Equation, Nets, and Hypergeometric Functions

V. Turaev, I. Frenkel, 1995 .