The Steinberg Tensor Product Theorem for General Linear Group Schemes in the Verlinde Category
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909346401615872 |
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| author | Kannan, Arun S. |
| author_facet | Kannan, Arun S. |
| contents | The Steinberg tensor product theorem is a fundamental result in the modular representation theory of reductive algebraic groups. It describes any finite-dimensional simple module of highest weight $λ$ over such a group as the tensor product of Frobenius twists of simple modules with highest weights the weights appearing in a $p$-adic decomposition of $λ$, thereby reducing the character problem to a a finite collection of weights. In recent years this theorem has been extended to various quasi-reductive supergroup schemes. In this paper, we prove the analogous result for the general linear group scheme $GL(X)$ for any object $X$ in the Verlinde category $\mathrm{Ver}_p$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_02786 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Steinberg Tensor Product Theorem for General Linear Group Schemes in the Verlinde Category Kannan, Arun S. Representation Theory The Steinberg tensor product theorem is a fundamental result in the modular representation theory of reductive algebraic groups. It describes any finite-dimensional simple module of highest weight $λ$ over such a group as the tensor product of Frobenius twists of simple modules with highest weights the weights appearing in a $p$-adic decomposition of $λ$, thereby reducing the character problem to a a finite collection of weights. In recent years this theorem has been extended to various quasi-reductive supergroup schemes. In this paper, we prove the analogous result for the general linear group scheme $GL(X)$ for any object $X$ in the Verlinde category $\mathrm{Ver}_p$. |
| title | The Steinberg Tensor Product Theorem for General Linear Group Schemes in the Verlinde Category |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2404.02786 |