Minimal W-algebras with non-admissible levels and intermediate Lie algebras
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916295189987328 |
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| author | Sun, Kaiwen |
| author_facet | Sun, Kaiwen |
| contents | In \cite{Kawasetsu:2018irs}, Kawasetsu proved that the simple W-algebra associated with a minimal nilpotent element $W_{k}(\mathfrak{g},f_θ)$ is rational and $C_2$-cofinite for $\mathfrak{g}=D_4,E_6,E_7,E_8$ with non-admissible level $k=-h^\vee/6$. In this paper, we study ${W}_{k}(\mathfrak{g},f_θ)$ algebra for $\mathfrak{g}=E_6,E_7,E_8$ with non-admissible level $k=-h^\vee/6+1$. We determine all irreducible (Ramond twisted) modules, compute their characters and find coset constructions and Hecke operator interpretations. These W-algebras are closely related to intermediate Lie algebras and intermediate vertex subalgebras. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_04182 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Minimal W-algebras with non-admissible levels and intermediate Lie algebras Sun, Kaiwen Mathematical Physics High Energy Physics - Theory Quantum Algebra In \cite{Kawasetsu:2018irs}, Kawasetsu proved that the simple W-algebra associated with a minimal nilpotent element $W_{k}(\mathfrak{g},f_θ)$ is rational and $C_2$-cofinite for $\mathfrak{g}=D_4,E_6,E_7,E_8$ with non-admissible level $k=-h^\vee/6$. In this paper, we study ${W}_{k}(\mathfrak{g},f_θ)$ algebra for $\mathfrak{g}=E_6,E_7,E_8$ with non-admissible level $k=-h^\vee/6+1$. We determine all irreducible (Ramond twisted) modules, compute their characters and find coset constructions and Hecke operator interpretations. These W-algebras are closely related to intermediate Lie algebras and intermediate vertex subalgebras. |
| title | Minimal W-algebras with non-admissible levels and intermediate Lie algebras |
| topic | Mathematical Physics High Energy Physics - Theory Quantum Algebra |
| url | https://arxiv.org/abs/2406.04182 |