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Modular invariant representations of infinite-dimensional Lie algebras and superalgebras.

- V. Kac, M. Wakimoto
- MathematicsProceedings of the National Academy of Sciences…
- 1 July 1988

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Integrable Highest Weight Modules over Affine Superalgebras and Appell's Function

- V. Kac, M. Wakimoto
- Mathematics
- 7 June 2000

Abstract:We classify integrable irreducible highest weight representations of non-twisted affine Lie superalgebras. We give a free field construction in the level 1 case. The analysis of this… Expand

Quantum reduction and representation theory of superconformal algebras

- V. Kac, M. Wakimoto
- Mathematics
- 7 April 2003

Integrable Highest Weight Modules over Affine Superalgebras and Number Theory

- V. Kac, M. Wakimoto
- Mathematics
- 11 July 1994

The problem of representing an integer as a sum of squares of integers has had a long history. One of the first after antiquity was A. Girard who in 1632 conjectured that an odd prime p can be… Expand

Modular and conformal invariance constraints in representation theory of affine algebras

- V. Kac, M. Wakimoto
- Mathematics
- 1 August 1988

Fock representations of the affine Lie algebraA1(1)

- M. Wakimoto
- Mathematics
- 1 December 1986

The aim of this note is to show that the affine Lie algebraA1(1) has a natural family πμ, υ,v of Fock representations on the spaceC[xi,yj;i ∈ ℤ andj ∈ ℕ], parametrized by (μ,v) ∈C2. By corresponding… Expand

Quantum Reduction for Affine Superalgebras

- V. Kac, S. Roan, M. Wakimoto
- Mathematics
- 7 February 2003

We extend the homological method of quantization of generalized Drinfeld–Sokolov reductions to affine superalgebras. This leads, in particular, to a unified representation theory of superconformal… Expand

Characters and fusion rules forW-algebras via quantized Drinfeld-Sokolov reduction

- E. Frenkel, V. Kac, M. Wakimoto
- Mathematics
- 1 July 1992

Using the cohomological approach toW-algebras, we calculate characters and fusion coefficients for their representations obtained from modular invariant representations of affine algebras by the… Expand

On Rationality of W-algebras

- V. Kac, M. Wakimoto
- Mathematics
- 14 November 2007

We study the problem of classification of triples ($ \mathfrak{g} $; f; k), where g is a simple Lie algebra, f its nilpotent element and k ∈ $ \mathbb{C} $, for which the simple W-algebra Wk($… Expand

On E 10

- V. Kac, R. Moody, M. Wakimoto
- Mathematics
- 1988

The simply-laced exceptional simple Lie algebras form part of an infinite series of Kac-Moody Lie algebras
$${A_2} \times {A_1},\quad {A_4},\quad {D_5},\quad {E_6},\quad {E_7},\quad {E_8},\quad… Expand

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