English

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