Cuspidal modules over Superconformal algebras of rank \geq 1
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916761779044352 |
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| author | Martinez, Consuelo Mathieu, Olivier Zelmanov, Efim |
| author_facet | Martinez, Consuelo Mathieu, Olivier Zelmanov, Efim |
| contents | According to V. Kac and J. van de Leur, the superconformal algebras are the simple $\Z$-graded Lie superalgebras of growth one which contains the Witt algebra. We describe an explicit classification of all cuspidal modules over the known supercuspidal algebras of rank $\geq 1$, and their central extensions.
Our approach reveals some unnoticed phenomena. Indeed the central charge of cuspidal modules is trivial, except for one specific central extension of the contact algebra $\K(4)$. As shown in the paper, this fact also impacts the representation theory of $\K(3)$, $\CK(6)$ and $\K^{(2)}(4)$.
Besides these four cases, the classification relies on general methods based on highest weight theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_20974 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cuspidal modules over Superconformal algebras of rank \geq 1 Martinez, Consuelo Mathieu, Olivier Zelmanov, Efim Representation Theory 17B68, 17B65, 17B70 According to V. Kac and J. van de Leur, the superconformal algebras are the simple $\Z$-graded Lie superalgebras of growth one which contains the Witt algebra. We describe an explicit classification of all cuspidal modules over the known supercuspidal algebras of rank $\geq 1$, and their central extensions. Our approach reveals some unnoticed phenomena. Indeed the central charge of cuspidal modules is trivial, except for one specific central extension of the contact algebra $\K(4)$. As shown in the paper, this fact also impacts the representation theory of $\K(3)$, $\CK(6)$ and $\K^{(2)}(4)$. Besides these four cases, the classification relies on general methods based on highest weight theory. |
| title | Cuspidal modules over Superconformal algebras of rank \geq 1 |
| topic | Representation Theory 17B68, 17B65, 17B70 |
| url | https://arxiv.org/abs/2505.20974 |