Unitarity of minimal $W$-algebras and their representations II: Ramond sector
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866908851319603200 |
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| author | Kac, Victor G. Frajria, Pierluigi Möseneder Papi, Paolo |
| author_facet | Kac, Victor G. Frajria, Pierluigi Möseneder Papi, Paolo |
| contents | In this paper we study unitary Ramond twisted representations of minimal $W$-algebras. We classify all such irreducible highest weight representations with a non-Ramond extremal highest weight (unitarity in the Ramond extremal case, as well as in the untwisted extremal case, remains open). We compute the characters of these representations and deduce from them the denominator identities for all superconformal algebras in the Neveu-Schwarz and Ramond sector. Some of the results rely on conjectures about the properties of the quantum Hamiltonian reduction functor in the Ramond sector. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_19090 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Unitarity of minimal $W$-algebras and their representations II: Ramond sector Kac, Victor G. Frajria, Pierluigi Möseneder Papi, Paolo Representation Theory Quantum Algebra In this paper we study unitary Ramond twisted representations of minimal $W$-algebras. We classify all such irreducible highest weight representations with a non-Ramond extremal highest weight (unitarity in the Ramond extremal case, as well as in the untwisted extremal case, remains open). We compute the characters of these representations and deduce from them the denominator identities for all superconformal algebras in the Neveu-Schwarz and Ramond sector. Some of the results rely on conjectures about the properties of the quantum Hamiltonian reduction functor in the Ramond sector. |
| title | Unitarity of minimal $W$-algebras and their representations II: Ramond sector |
| topic | Representation Theory Quantum Algebra |
| url | https://arxiv.org/abs/2405.19090 |