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arXiv · 2006.01493

Branching rules and commuting probabilities for Triangular and Unitriangular matrices

Dilpreet Kaur·Uday Bhaskar Sharma·Anupam Singh
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Abstract

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.

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Dilpreet Kaur, Uday Bhaskar Sharma, Anupam Singh. 2020-06-02. Branching rules and commuting probabilities for Triangular and Unitriangular matrices. https://doi.org/10.1142/s0219498822502310

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