Sharp character bounds for symmetric groups in terms of partition length
| Autor: | Larsen, Michael |
|---|---|
| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Let $S_n$ denote a symmetric group, $\chi$ an irreducible character of $S_n$, and $g\in S_n$ an element which decomposes into $k$ disjoint cycles, where $1$-cycles are included. Then $|\chi(g)|\le k!$, and this upper bound is sharp for fixed $k$ and varying $n$, $\chi$, and $g$. This implies a sharp upper bound of $k!$ for unipotent character values of $SL_n(q)$ at regular semisimple elements with characteristic polynomial $P(t)=P_1(t)\cdots P_k(t)$, where the $P_i$ are irreducible over $F_q[t]$. Comment: 7 pages |
| Databáze: | arXiv |
| Externí odkaz: |
|