Basic sets for the double covering groups of the symmetric and alternating groups in odd characteristic

TL;DR

This paper demonstrates that the double covering groups of symmetric and alternating groups possess p-basic sets for any odd prime p, extending understanding of their modular representation theory.

Contribution

It establishes the existence of p-basic sets for these groups in odd characteristic, building on previous methods and expanding the theoretical framework.

Findings

Existence of p-basic sets for double covering groups in odd characteristic

Extension of previous methods to new classes of groups

Advancement in modular representation theory of covering groups

Abstract

In this paper, following the methods of http://arxiv.org/abs/1305.7449v2, we show that the double covering groups of the symmetric and alternating groups have p-basic sets for any odd prime p.