Multiplicity free and completely reducible tensor products for $\mathrm{SL}_3(\Bbbk)$ and $\mathrm{Sp}_4(\Bbbk)$
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914955099373568 |
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| author | Gruber, Jonathan Mancini, Gaëtan |
| author_facet | Gruber, Jonathan Mancini, Gaëtan |
| contents | Let $G$ be a simple algebraic group over an algebraically closed field $\Bbbk$ of positive characteristic. We consider the questions of when the tensor product of two simple $G$-modules is multiplicity free or completely reducible. We develop tools for answering these questions in general, and we use them to provide complete answers for the groups $G = \mathrm{SL}_3(\Bbbk)$ and $G = \mathrm{Sp}_4(\Bbbk)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_07888 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Multiplicity free and completely reducible tensor products for $\mathrm{SL}_3(\Bbbk)$ and $\mathrm{Sp}_4(\Bbbk)$ Gruber, Jonathan Mancini, Gaëtan Representation Theory 20G05 (primary), 51F15 (secondary) Let $G$ be a simple algebraic group over an algebraically closed field $\Bbbk$ of positive characteristic. We consider the questions of when the tensor product of two simple $G$-modules is multiplicity free or completely reducible. We develop tools for answering these questions in general, and we use them to provide complete answers for the groups $G = \mathrm{SL}_3(\Bbbk)$ and $G = \mathrm{Sp}_4(\Bbbk)$. |
| title | Multiplicity free and completely reducible tensor products for $\mathrm{SL}_3(\Bbbk)$ and $\mathrm{Sp}_4(\Bbbk)$ |
| topic | Representation Theory 20G05 (primary), 51F15 (secondary) |
| url | https://arxiv.org/abs/2409.07888 |