The Divisibility of $\mathrm{GL}(n, q)$ Character Values
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913481641426944 |
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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 |