The Kazhdan-Lusztig conjecture for W algebras
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.
- Publication:
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Journal of Mathematical Physics
- Pub Date:
- July 1996
- DOI:
- 10.1063/1.531584
- arXiv:
- arXiv:hep-th/9508020
- Bibcode:
- 1996JMP....37.3587D
- Keywords:
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- High Energy Physics - Theory
- E-Print:
- uuencoded file, 29 pages latex, 5 figures