Unitriangular basic sets for blocks of the symmetric and alternating groups of small weights
Combinatorics
2021-11-23 v2 Representation Theory
Abstract
We study the existence of unitriangular basic sets for the symmetric group which behave nicely with respect to the Mullineux involution. Such sets give a natural labelling for the modular irreducible representations. We show that, for any odd prime p, the p-blocks of the symmetric group with weight 2 have stable unitriangular basic sets which we describe by studying the combinatorics of partitions in these blocks.
Cite
@article{arxiv.2106.07215,
title = {Unitriangular basic sets for blocks of the symmetric and alternating groups of small weights},
author = {Ana Bernal},
journal= {arXiv preprint arXiv:2106.07215},
year = {2021}
}