Branching rules and commuting probabilities for Triangular and Unitriangular matrices

Abstract

This paper concerns the enumeration of simultaneous conjugacy classes of $k$-tuples of commuting matrices in the upper triangular group $G{T}_n({\mathbf{F}}_q)$ and unitriangular group $U{T}_m({\mathbf{F}}_q)$ 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 $c{p}_k$ for $k\le 5$ in each case.

References in corpus (3)

• Simultaneous Similarity Classes of Commuting matrices over a finite field
• Commuting probability and simultaneous conjugacy classes of commuting tuples in a group
• Branching rules for Unitary and Symplectic matrices