Characters and projective characters of alternating and symmetric groups determined by values on $l'$-classes

Autor:	McDowell, Eoghan
Rok vydání:	2022
Předmět:	Mathematics - Representation Theory Mathematics - Group Theory 20C15 (Primary) 20C20 20C30 (Secondary)
Druh dokumentu:	Working Paper
Popis:	This paper identifies all pairs of ordinary irreducible characters of the alternating group which agree on conjugacy classes of elements of order not divisible by a fixed integer $l$, for $l \neq 3$. We do the same for the double covers of the symmetric and alternating groups. The only such characters are the conjugate or associate pairs labelled by partitions with a certain parameter divisible by $l$. When $l$ is prime, this implies that the rows of the $l$-modular decomposition matrix are distinct except for the rows labelled by these pairs. When $l=3$ we exhibit many additional examples of such pairs of characters. Comment: 15 pages (accepted manuscript version)
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2205.06505 Zobrazit plný text záznamu View this record from Arxiv