On tensor products of representations of Lie superalgebras
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866916186220920832 |
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| author | Das, Abhishek Pattanayak, Santosha |
| author_facet | Das, Abhishek Pattanayak, Santosha |
| contents | We consider typical finite dimensional complex irreducible representations of a basic classical simple Lie superalgebra, and give a sufficient condition on when unique factorization of finite tensor products of such representations hold. We also prove unique factorization of tensor products of singly atypical finite dimensional irreducible modules for $\mathfrak{sl}(m+1,n+1)$, $\mathfrak{osp}(2,2n)$, $G(3)$ and $F(4)$ under an additional assumption. This result is a Lie superalgebra analogue of Rajan's fundamental result \cite{MR2123935} on unique factorization of tensor products for finite dimensional complex simple Lie algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_00266 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On tensor products of representations of Lie superalgebras Das, Abhishek Pattanayak, Santosha Representation Theory 17B05, 17B10, 17B65 We consider typical finite dimensional complex irreducible representations of a basic classical simple Lie superalgebra, and give a sufficient condition on when unique factorization of finite tensor products of such representations hold. We also prove unique factorization of tensor products of singly atypical finite dimensional irreducible modules for $\mathfrak{sl}(m+1,n+1)$, $\mathfrak{osp}(2,2n)$, $G(3)$ and $F(4)$ under an additional assumption. This result is a Lie superalgebra analogue of Rajan's fundamental result \cite{MR2123935} on unique factorization of tensor products for finite dimensional complex simple Lie algebras. |
| title | On tensor products of representations of Lie superalgebras |
| topic | Representation Theory 17B05, 17B10, 17B65 |
| url | https://arxiv.org/abs/2404.00266 |