Block decomposition via the geometric Satake equivalence
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866908928653131776 |
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| author | Zabeth, Emilien |
| author_facet | Zabeth, Emilien |
| contents | We give a new proof for the description of the blocks in the category of representations of a reductive algebraic group $\mathbf{G}$ over a field of positive characteristic $\ell$ (originally due to Donkin), by working in the Satake category of the Langlands dual group and applying Smith-Treumann theory as developed by Riche and Williamson. On the representation theoretic side, our methods enable us to give a bound for the length of a minimum chain linking two weights in the same block, and to give a new proof for the block decomposition of a quantum group at an $\ell$-th root of unity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_06184 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Block decomposition via the geometric Satake equivalence Zabeth, Emilien Representation Theory We give a new proof for the description of the blocks in the category of representations of a reductive algebraic group $\mathbf{G}$ over a field of positive characteristic $\ell$ (originally due to Donkin), by working in the Satake category of the Langlands dual group and applying Smith-Treumann theory as developed by Riche and Williamson. On the representation theoretic side, our methods enable us to give a bound for the length of a minimum chain linking two weights in the same block, and to give a new proof for the block decomposition of a quantum group at an $\ell$-th root of unity. |
| title | Block decomposition via the geometric Satake equivalence |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2207.06184 |