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| Main Author: | |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2307.15628 |
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| _version_ | 1866913332165869568 |
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| author | Marko, František |
| author_facet | Marko, František |
| contents | We present rational Schur algebra $S(n,r,s)$ over an arbitrary ground field $K$ as a quotient of the distribution algebra $Dist(G)$ of the general linear group $G=GL(n)$ by an ideal $I(n,r,s)$ and provide an explicit description of the generators of $I(n,r,s)$. Over fields $K$ of characteristic zero, this corrects and completes a presentation of $S(n,r,s)$ in terms of generators and relations originally considered by Dipper and Doty. The explicit presentation over ground fields of positive characteristics appears here for the first time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_15628 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Presentation of rational Schur algebras Marko, František Representation Theory We present rational Schur algebra $S(n,r,s)$ over an arbitrary ground field $K$ as a quotient of the distribution algebra $Dist(G)$ of the general linear group $G=GL(n)$ by an ideal $I(n,r,s)$ and provide an explicit description of the generators of $I(n,r,s)$. Over fields $K$ of characteristic zero, this corrects and completes a presentation of $S(n,r,s)$ in terms of generators and relations originally considered by Dipper and Doty. The explicit presentation over ground fields of positive characteristics appears here for the first time. |
| title | Presentation of rational Schur algebras |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2307.15628 |