On complete reducibility for infinite-dimensional Lie algebras
In this paper we study the complete reducibility of representations of infinite-dimensional Lie algebras from the perspective of the representation theory of vertex algebras.
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arXiv subjects
M. Gorelik
Publications and source records attributed to M. Gorelik.
Characters of highest weight modules over affine Lie algebras are meromorphic functions
We show that the characters of all highest weight modules over an affine Lie algebra with the highest weight away from the critical hyperplane are meromorphic functions in the positive half of Cartan subalgebra, their singularities being at most simple poles at zeros of real roots. We obtain some information about these singularities.
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On simplicity of vacuum modules
We find necessary and sufficient conditions of irreducibility of vacuum modules over affine Lie algebras and superalgebras. From this we derive conditions of simplicity of minimal W-algebras. Moreover, in the case of Virasoro and Neveu-Schwarz algebras we obtain explicit formulas for vacuum determinants.
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