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Modular invariant representations of infinite-dimensional Lie algebras and superalgebras.
  • V. Kac, M. Wakimoto
  • Mathematics
    Proceedings of the National Academy of Sciences…
  • 1 July 1988
It is shown that the modular invariant representations of the Virasoro algebra Vir are precisely the "minimal series" of Belavin et al.
Integrable Highest Weight Modules over Affine Superalgebras and Appell's Function
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
Integrable Highest Weight Modules over Affine Superalgebras and Number Theory
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
Fock representations of the affine Lie algebraA1(1)
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
Quantum Reduction for Affine Superalgebras
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
Characters and fusion rules forW-algebras via quantized Drinfeld-Sokolov reduction
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
On Rationality of W-algebras
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} $, for which the simple W-algebra Wk($
On E 10
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