Quantized Reductions and Irreducible Representations of W-Algebras

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.

22 pages, fixed font problems

References in corpus (5)

• Vertex Algebras and Algebraic Curves
• The Relation between Quantum W algebras and Lie algebras
• Freely generated vertex algebras and non-linear Lie conformal algebras
• Characters of irreducible modules with non-critical highest weights over affine Lie algebras
• Vanishing of cohomology associated to quantized Drinfeld-Sokolov reduction