Branching rules and commuting probabilities for Triangular and Unitriangular matrices
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2020
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| _version_ | 1866916189740990464 |
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| author | Kaur, Dilpreet Sharma, Uday Bhaskar Singh, Anupam |
| author_facet | Kaur, Dilpreet Sharma, Uday Bhaskar Singh, Anupam |
| contents | This paper concerns the enumeration of simultaneous conjugacy classes of $k$-tuples of commuting matrices in the upper triangular group $GT_n(\mathbf F_q)$ and unitriangular group $UT_m(\mathbf F_q)$ over the finite field $\mathbf F_q$ of odd characteristic. This is done for $n=2,3,4$ and $m=3,4,5$, by computing the branching rules. Further, using the branching matrix thus computed, we explicitly get the commuting probabilities $cp_k$ for $k\leq 5$ in each case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2006_01493 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Branching rules and commuting probabilities for Triangular and Unitriangular matrices Kaur, Dilpreet Sharma, Uday Bhaskar Singh, Anupam Group Theory 05A05, 20G40, 20E45 This paper concerns the enumeration of simultaneous conjugacy classes of $k$-tuples of commuting matrices in the upper triangular group $GT_n(\mathbf F_q)$ and unitriangular group $UT_m(\mathbf F_q)$ over the finite field $\mathbf F_q$ of odd characteristic. This is done for $n=2,3,4$ and $m=3,4,5$, by computing the branching rules. Further, using the branching matrix thus computed, we explicitly get the commuting probabilities $cp_k$ for $k\leq 5$ in each case. |
| title | Branching rules and commuting probabilities for Triangular and Unitriangular matrices |
| topic | Group Theory 05A05, 20G40, 20E45 |
| url | https://arxiv.org/abs/2006.01493 |