Semisimplifications and representations of the General Linear Supergroup
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917909552431104 |
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| author | Heidersdorf, Thorsten Weissauer, Rainer |
| author_facet | Heidersdorf, Thorsten Weissauer, Rainer |
| contents | We study the semisimplification of the full karoubian subcategory generated by the irreducible finite dimensional representations of the algebraic supergroup $GL(m|n)$ over an algebraically closed field of characteristic zero. This semisimplification is equivalent to the representations of a pro-reductive group $H_{m|n}$. We show that there is a canonical decomposition $H_{m|n} \cong GL(m\!-\! n) \times H_{n|n}$, thereby reducing the determination of $H_{m|n}$ to the equal rank case $m\! =\! n$ which was treated in a previous paper. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_05298 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Semisimplifications and representations of the General Linear Supergroup Heidersdorf, Thorsten Weissauer, Rainer Representation Theory Mathematical Physics 17B10, 17B20, 17B55, 18M05, 18M25, 20G05 We study the semisimplification of the full karoubian subcategory generated by the irreducible finite dimensional representations of the algebraic supergroup $GL(m|n)$ over an algebraically closed field of characteristic zero. This semisimplification is equivalent to the representations of a pro-reductive group $H_{m|n}$. We show that there is a canonical decomposition $H_{m|n} \cong GL(m\!-\! n) \times H_{n|n}$, thereby reducing the determination of $H_{m|n}$ to the equal rank case $m\! =\! n$ which was treated in a previous paper. |
| title | Semisimplifications and representations of the General Linear Supergroup |
| topic | Representation Theory Mathematical Physics 17B10, 17B20, 17B55, 18M05, 18M25, 20G05 |
| url | https://arxiv.org/abs/2501.05298 |