The Divisibility of $\mathrm{GL}(n, q)$ Character Values

Fuente: arXiv
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Autori principali: Shah, Varun, Spallone, Steven
Natura: Preprint
Pubblicazione: 2024
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author Shah, Varun
Spallone, Steven
author_facet Shah, Varun
Spallone, Steven
contents Let $q$ be a prime power, and $d$ a positive integer. We study the proportion of irreducible characters of $\mathrm{GL}(n,q)$ whose values evaluated on a fixed matrix $g$ are divisible by $d$. As $n$ approaches infinity, this proportion tends to $1$ when $q$ is coprime to $d$. When $q$ and $d$ are not coprime, and $g=1$, this proportion is bounded above by $\frac{1}{q}$.
format Preprint
id arxiv_https___arxiv_org_abs_2408_14046
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle The Divisibility of $\mathrm{GL}(n, q)$ Character Values
Shah, Varun
Spallone, Steven
Representation Theory
Combinatorics
Let $q$ be a prime power, and $d$ a positive integer. We study the proportion of irreducible characters of $\mathrm{GL}(n,q)$ whose values evaluated on a fixed matrix $g$ are divisible by $d$. As $n$ approaches infinity, this proportion tends to $1$ when $q$ is coprime to $d$. When $q$ and $d$ are not coprime, and $g=1$, this proportion is bounded above by $\frac{1}{q}$.
title The Divisibility of $\mathrm{GL}(n, q)$ Character Values
topic Representation Theory
Combinatorics
url https://arxiv.org/abs/2408.14046