Conjugacy action, induced representations and the Steinberg square for simple groups of Lie type

Autor:	Heide, Gerhard, Saxl, Jan, Tiep, Pham Huu, Zalesski, Alexandre E.
Rok vydání:	2012
Předmět:	Mathematics - Group Theory Mathematics - Representation Theory 20C33 20C15
Druh dokumentu:	Working Paper
DOI:	10.1112/plms/pds062
Popis:	Let $G$ be a finite simple group of Lie type, and let $\pi_G$ be the permutation representation of $G$ associated with the action of $G$ on itself by conjugation. We prove that every irreducible representation of $G$ is a constituent of $\pi_G$, unless $G=PSU_n(q)$ and $n$ is coprime to $2(q+1)$, where precisely one irreducible representation fails. Let St be the Steinberg representation of $G$. We prove that a complex irreducible representation of $G$ is a constituent of the tensor square $St\otimes St$, with the same exceptions as in the previous statement. Comment: To appear in the Proceedings of the London Mathematical Society
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1209.1768 Zobrazit plný text záznamu View this record from Arxiv