Representation theory of W-algebras, II: Ramond twisted representations

Details Representation theory of W-algebras, II: Ramond twisted representations Representation theory of W-algebras, II: Ramond twisted representations

2008-02-12

arxiv.org/abs/0802.1564v2

Mathematics

Quantum Algebra

Fixed some errors

Scientific paper

We study the Ramond twisted representations of the affine W-algebra W^k(g,f) in the case that f admits a good even grading. We establish the vanishing and the almost irreducibility of the corresponding BRST cohomology. This confirms some of the recent conjectures of Kac and Wakimoto. In type A, our results give the characters of all irreducible ordinary Ramond twisted representations of W^k(sl_n,f) for all nilpotent elements f and all non-critical k, and prove the existence of modular invariant representations conjectured by Kac and Wakimoto.

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