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| Format: | Preprint |
| Publié: |
2025
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| Accès en ligne: | https://arxiv.org/abs/2508.00488 |
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| _version_ | 1866918382465449984 |
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| author | Dong, Junbin |
| author_facet | Dong, Junbin |
| contents | Let ${\bf G}$ be a connected reductive algebraic group defined over the finite field $\mathbb{F}_q$ with $q$ elements. We propose some conjectures concerning the simple quotients of $M\otimes N$, where $M,N$ are objects in the representation category $\mathscr{X}({\bf G})$ introduced by the author in a previous work to study the complex representations of ${\bf G}$. We provide several pieces of evidence for these conjectures. In particular, we show that these conjectures are valid for ${\bf G}=SL_2(\bar{\mathbb{F}}_q)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_00488 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Some conjectures on the quotients of the tensor products in the category $\mathscr{X}$ Dong, Junbin Representation Theory Let ${\bf G}$ be a connected reductive algebraic group defined over the finite field $\mathbb{F}_q$ with $q$ elements. We propose some conjectures concerning the simple quotients of $M\otimes N$, where $M,N$ are objects in the representation category $\mathscr{X}({\bf G})$ introduced by the author in a previous work to study the complex representations of ${\bf G}$. We provide several pieces of evidence for these conjectures. In particular, we show that these conjectures are valid for ${\bf G}=SL_2(\bar{\mathbb{F}}_q)$. |
| title | Some conjectures on the quotients of the tensor products in the category $\mathscr{X}$ |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2508.00488 |