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Representation Theory of W-Algebras

Quantum Algebra 2007-06-13 v4 Mathematical Physics math.MP Representation Theory

Abstract

This paper is the detailed version of math.QA/0403477 (T. Arakawa, Quantized Reductions and Irreducible Representations of W-Algebras) with extended results; We study the representation theory of the W-algebra Wk(g)W_k(g) associated with a simple Lie algebra gg (and its principle nilpotent element) at level k. We show that the "-" reduction functor is exact and sends an irreducible module to zero or an irreducible module at any level k. Moreover, we show that the character of each irreducible highest weight representation of Wk(g)W_k(g) is completely determined by that of the corresponding irreducible highest weight representation of affine Lie algebra of gg.

Keywords

Cite

@article{arxiv.math/0506056,
  title  = {Representation Theory of W-Algebras},
  author = {Tomoyuki Arakawa},
  journal= {arXiv preprint arXiv:math/0506056},
  year   = {2007}
}

Comments

replaced by published version. pulished on line in Invent. Math. The original publication is available at http://www.springerlink.com