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| Format: | Preprint |
| Publié: |
2023
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2309.15967 |
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| _version_ | 1866916542485102592 |
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| author | Hayashi, Takuma |
| author_facet | Hayashi, Takuma |
| contents | In this paper, we classify irreducible representations of affine group superschemes over fields $F$ of characteristic not two in terms of those over a separable closure $F^{\mathrm{sep}}$ and their Galois twists. We also compute the division superalgebras of their endomorphisms. Finally, we give numerical conclusions for quasi-reductive algebraic supergroups under certain conditions, based on Shibata's Borel--Weil theory for split quasi-reductive algebraic supergroups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_15967 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Classification of irreducible representations of affine group superschemes and the division superalgebras of their endomorphisms Hayashi, Takuma Representation Theory In this paper, we classify irreducible representations of affine group superschemes over fields $F$ of characteristic not two in terms of those over a separable closure $F^{\mathrm{sep}}$ and their Galois twists. We also compute the division superalgebras of their endomorphisms. Finally, we give numerical conclusions for quasi-reductive algebraic supergroups under certain conditions, based on Shibata's Borel--Weil theory for split quasi-reductive algebraic supergroups. |
| title | Classification of irreducible representations of affine group superschemes and the division superalgebras of their endomorphisms |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2309.15967 |