Commuting matrices via commuting endomorphisms
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916229938151424 |
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| author | Huang, Yifeng |
| author_facet | Huang, Yifeng |
| contents | Evidences have suggested that counting representations are sometimes tractable even when the corresponding classification problem is almost impossible, or "wild" in a precise sense. Such counting problems are directly related to matrix counting problems, many of which are under active research. Using a general framework we formulate for such counting problems, we reduce some counting problems about commuting matries to problems about endomorphisms on all finite abelian $p$-groups. As an application, we count finite modules on some first examples of nonreduced curves over $\mathbb{F}_q$. We also relate some classical and hard problems regarding commuting triples of matrices to a conjecture of Onn on counting conjugacy classes of the automorphism group of an arbitrary finite abelian $p$-group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_19483 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Commuting matrices via commuting endomorphisms Huang, Yifeng Representation Theory Combinatorics 05A15, 15A24, 20K30 Evidences have suggested that counting representations are sometimes tractable even when the corresponding classification problem is almost impossible, or "wild" in a precise sense. Such counting problems are directly related to matrix counting problems, many of which are under active research. Using a general framework we formulate for such counting problems, we reduce some counting problems about commuting matries to problems about endomorphisms on all finite abelian $p$-groups. As an application, we count finite modules on some first examples of nonreduced curves over $\mathbb{F}_q$. We also relate some classical and hard problems regarding commuting triples of matrices to a conjecture of Onn on counting conjugacy classes of the automorphism group of an arbitrary finite abelian $p$-group. |
| title | Commuting matrices via commuting endomorphisms |
| topic | Representation Theory Combinatorics 05A15, 15A24, 20K30 |
| url | https://arxiv.org/abs/2404.19483 |