Uniform Character Bounds for Finite Classical Groups
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866913264525377536 |
|---|---|
| author | Larsen, Michael Tiep, Pham Huu |
| author_facet | Larsen, Michael Tiep, Pham Huu |
| contents | For every finite quasisimple group of Lie type $G$, every irreducible character $χ$ of $G$, and every element $g$ of $G$, we give an exponential upper bound for the character ratio $|χ(g)|/χ(1)$ with exponent linear in $\log_{|G|} |g^G|$, or, equivalently, in the ratio of the support of $g$ to the rank of $G$. We give several applications, including a proof of Thompson's conjecture for all sufficiently large simple symplectic groups, orthogonal groups in characteristic $2$, and some other infinite families of orthogonal and unitary groups |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_09046 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Uniform Character Bounds for Finite Classical Groups Larsen, Michael Tiep, Pham Huu Representation Theory Group Theory 20C33, 20D06, 20G40, 20P05 For every finite quasisimple group of Lie type $G$, every irreducible character $χ$ of $G$, and every element $g$ of $G$, we give an exponential upper bound for the character ratio $|χ(g)|/χ(1)$ with exponent linear in $\log_{|G|} |g^G|$, or, equivalently, in the ratio of the support of $g$ to the rank of $G$. We give several applications, including a proof of Thompson's conjecture for all sufficiently large simple symplectic groups, orthogonal groups in characteristic $2$, and some other infinite families of orthogonal and unitary groups |
| title | Uniform Character Bounds for Finite Classical Groups |
| topic | Representation Theory Group Theory 20C33, 20D06, 20G40, 20P05 |
| url | https://arxiv.org/abs/2403.09046 |