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VOL. 61 | 2011 Representation theory of $W$-algebras, II
Tomoyuki Arakawa

Editor(s) Koji Hasegawa, Takahiro Hayashi, Shinobu Hosono, Yasuhiko Yamada

Abstract

We study the (Ramond twisted) representations of the affine $W$-algebra $\mathcal{W}^k (\bar{\mathfrak{g}}, f)$ 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 [KW08]. In type $A$, our results give the characters of all irreducible ordinary (Ramond twisted) representations of $\mathcal{W}^k (\mathfrak{sl}_n, f)$ for all nilpotent elements $f$ and all non-critical $k$, and prove the existence of modular invariant representations conjectured in [KW08].

Information

Published: 1 January 2011
First available in Project Euclid: 24 November 2018

zbMATH: 1262.17014
MathSciNet: MR2867144

Digital Object Identifier: 10.2969/aspm/06110051

Keywords: W-algebras

Rights: Copyright © 2011 Mathematical Society of Japan

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