Representation theory of W-algebras, II: Ramond twisted representations
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arXiv
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| Format: | Preprint |
| Publié: |
2008
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| _version_ | 1866910329496141824 |
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| author | Arakawa, Tomoyuki |
| author_facet | Arakawa, Tomoyuki |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_0802_1564 |
| institution | arXiv |
| publishDate | 2008 |
| record_format | arxiv |
| spellingShingle | Representation theory of W-algebras, II: Ramond twisted representations Arakawa, Tomoyuki Quantum Algebra Mathematical Physics Representation Theory 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. |
| title | Representation theory of W-algebras, II: Ramond twisted representations |
| topic | Quantum Algebra Mathematical Physics Representation Theory |
| url | https://arxiv.org/abs/0802.1564 |