Quantized Reductions and Irreducible Representations of W-Algebras

Details Quantized Reductions and Irreducible Representations of W-Algebras Quantized Reductions and Irreducible Representations of W-Algebras

2004-03-27

arxiv.org/abs/math/0403477v2

Mathematics

Quantum Algebra

22 pages, fixed font problems

Scientific paper

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.

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