Irreducible tensor products for alternating groups in characteristic 2

TL;DR

This paper fully classifies when tensor products of basic spin modules with irreducible modules of alternating groups remain irreducible in characteristic 2, advancing the understanding of their representation theory.

Contribution

It provides a complete characterization of irreducible tensor products involving basic spin modules for alternating groups in characteristic 2, filling a key gap in the classification.

Findings

Complete classification of irreducible tensor products in characteristic 2

Identification of conditions for irreducibility of tensor products

Advancement in the representation theory of alternating groups

Abstract

In this paper we completely characterise irreducible tensor products of representations of alternating groups in characteristic 2 of a basic spin module with an irreducible module. This completes the classification of irreducible tensor products of representations of alternating groups.