Quantized Reductions and Irreducible Representations of W-Algebras
Quantum Algebra
2007-05-23 v2
Abstract
We study the representations of the W-algebra W(g) associated to an arbitrary finite-dimensional simple Lie algebra g via the quantized Drinfeld-Sokolov reductions. The characters of irreducible representations with non-degenerate highest weights are expressed by Kazhdan-Lusztig polynomials. The irreduciblity conjecture of Frenkel, Kac and Wakimoto is proved completely for the "-" reduction and partially for the "+" reduction. In particular, the existence of the minimal series representations (= the modular invariant representations) of W(g) is proved.
Keywords
Cite
@article{arxiv.math/0403477,
title = {Quantized Reductions and Irreducible Representations of W-Algebras},
author = {Tomoyuki Arakawa},
journal= {arXiv preprint arXiv:math/0403477},
year = {2007}
}
Comments
22 pages, fixed font problems