On the irreducible spin representations of symmetric and alternating groups which remain irreducible in characteristic 3

authored by

Matthew Fayers, Lucia Morotti

Abstract

For any finite group G and any prime p one can ask which ordinary irreducible representations remain irreducible in characteristic p, or more generally, which representations remain homogeneous in characteristic p. In this paper we address this question when G is a proper double cover of the symmetric or alternating group. We obtain a classification when p = 3 except in the case of a certain family of partitions relating to spin RoCK blocks. Our techniques involve induction and restriction, degree calculations, decomposing projective characters and recent results of Kleshchev and Livesey on spin RoCK blocks.

Organisation(s)

Institute of Algebra, Number Theory and Discrete Mathematics

External Organisation(s)

Queen Mary University of London

Type

Article

Journal

Representation theory

Volume

27

Pages

778-814

No. of pages

37

ISSN

1088-4165

Publication date

2023

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Mathematics (miscellaneous)

Electronic version(s)

https://doi.org/10.1090/ert/654 (Access: Open)