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We present an explicit character formula for the irreducible highest weight representations of the non-twisted affine Kac-Moody Lie algebra at the critical level which are integrable over the corresponding finite-dimensional simple Lie algebra.
Infinite-dimensional Lie algebras, and the Dedekind η \eta -function
V. G. Kac · 1974
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On Whittaker vectors and representation theory
Bertram Kostant · 1978
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Structure of representations with highest weight of infinite-dimensional Lie algebras
V. G. Kac and D. A. Kazhdan · 1979
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David Kazhdan and George Lusztig · 1979
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Minoru Wakimoto · 1986
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B. L. Feĭgin and È. V. Frenkel ′ · 1988
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Takahiro Hayashi · 1988
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Modular invariant representations of infinite-dimensional Lie algebras and superalgebras
Victor G. Kac and Minoru Wakimoto · 1988
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Higher-order Sugawara operators for affine Lie algebras
Roe Goodman and Nolan R. Wallach · 1989
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Structure of the Verma module M ( − ρ ) M(-\rho) over Euclidean Lie algebras
Jong Min Ku · 1989
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Classification of modular invariant representations of affine algebras
V. G. Kac and M. Wakimoto · 1989
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Quantization of the Drinfel ′
Boris Feigin and Edward Frenkel · 1990
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Affine Kac-Moody algebras and semi-infinite flag manifolds
Boris L. Feĭgin and Edward V. Frenkel · 1990
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Affine Kac-Moody algebras at the critical level and Gel ′
Boris Feigin and Edward Frenkel · 1992
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Characters and fusion rules for W W -algebras via quantized Drinfel ′
Edward Frenkel, Victor Kac, and Minoru Wakimoto · 1992
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Vertex operator algebras associated to representations of affine and Virasoro algebras
Igor B. Frenkel and Yongchang Zhu · 1992
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Kazhdan-Lusztig conjecture for affine Lie algebras with negative level
Masaki Kashiwara and Toshiyuki Tanisaki · 1995
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Proof of the Kazhdan-Lusztig conjecture for Kac-Moody algebras (the characters ch L w ρ − ρ \ch L_{w\rho-\rho} )
Chiral algebras
Alexander Beilinson and Vladimir Drinfeld · 2004
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Vertex algebras and algebraic curves
Edward Frenkel and David Ben-Zvi · 2004
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D D -modules on the affine Grassmannian and representations of affine Kac-Moody algebras
Edward Frenkel and Dennis Gaitsgory · 2004
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Opers on the projective line, flag manifolds and Bethe ansatz
Edward Frenkel · 2004
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Quantum reduction and representation theory of superconformal algebras
Victor G. Kac and Minoru Wakimoto · 2004
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Representation theory of superconformal algebras and the Kac-Roan-Wakimoto conjecture
Tomoyuki Arakawa · 2005
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Luis Casian · 1996
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Kazhdan-Lusztig conjecture for affine Lie algebras with negative level. II. Nonintegral case
Masaki Kashiwara and Toshiyuki Tanisaki · 1996
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Modular invariance of characters of vertex operator algebras
Yongchang Zhu · 1996
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Vertex algebras for beginners
Victor Kac · 1998
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Kazhdan-Lusztig conjecture for symmetrizable Kac-Moody Lie algebras. III. Positive rational case
Masaki Kashiwara and Toshiyuki Tanisaki · 1998
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Characters of irreducible modules with non-critical highest weights over affine Lie algebras
Masaki Kashiwara and Toshiyuki Tanisaki · 2000
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Quantum reduction for affine superalgebras
Victor Kac, Shi-Shyr Roan, and Minoru Wakimoto · 2003
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Localization of 𝔤 ^ \widehat{{\mathfrak{g}}} -modules on the affine grassmannian
Edward Frenkel and Dennis Gaitsgory · 2005
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Wakimoto modules, opers and the center at the critical level
Edward Frenkel · 2005
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Conformal field theories associated to regular chiral vertex operator algebras. I. Theories over the projective line
Kiyokazu Nagatomo and Akihiro Tsuchiya · 2005
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A new proof of the Kac-Kazhdan conjecture
Tomoyuki Arakawa · 2006
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Local geometric Langlands correspondence and affine Kac-Moody algebras
Edward Frenkel and Dennis Gaitsgory · 2006
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Ramifications of the geometric Langlands program
Edward Frenkel · 2006
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Representation theory of W W -algebras
Tomoyuki Arakawa · 2007
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