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The Kazhdan-Lusztig conjecture for W-algebras

Koos de Vos·Peter van Driel
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Abstract

The main result in this paper is the character formula for arbitrary irreducible highest weight modules of W algebras. The key ingredient is the functor provided by quantum Hamiltonian reduction, that constructs the W algebras from affine Kac-Moody algebras and in a similar fashion W modules from KM modules. Assuming certain properties of this functor, the W characters are subsequently derived from the Kazhdan-Lusztig conjecture for KM algebras. The result can be formulated in terms of a double coset of the Weyl group of the KM algebra: the Hasse diagrams give the embedding diagrams of the Verma modules and the Kazhdan-Lusztig polynomials give the multiplicities in the characters.

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Koos de Vos, Peter van Driel. 1995-08-04. The Kazhdan-Lusztig conjecture for W-algebras. https://doi.org/10.1063/1.531584

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