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

Abstract

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.

Fixed some errors

References in corpus (2)

• Representations of shifted Yangians and finite W-algebras
• Representation Theory of W-Algebras

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