Branching rules and commuting probabilities for Triangular and Unitriangular matrices

Fuente: arXiv
Gespeichert in:
Bibliographische Detailangaben
Hauptverfasser: Kaur, Dilpreet, Sharma, Uday Bhaskar, Singh, Anupam
Format: Preprint
Veröffentlicht: 2020
Schlagworte:
Online-Zugang:
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
_version_ 1866916189740990464
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