# Irreducible tensor products for alternating groups in characteristics 2 and 3

## TL;DR

This paper classifies irreducible tensor products of alternating group representations in characteristics 2 and 3, providing complete classifications in characteristic 3 and partial results in characteristic 2.

## Contribution

It offers a complete classification of irreducible tensor products in characteristic 3 and partial classifications in characteristic 2, advancing understanding of representation theory in these characteristics.

## Key findings

- Complete classification of irreducible tensor products in characteristic 3
- Partial classification in characteristic 2 for non-spin modules
- Necessary conditions for tensor products involving basic spin modules in characteristic 2

## Abstract

In this paper we study irreducible tensor products of representations of alternating groups in characteristics 2 and 3. In characteristic 3 we completely classify irreducible tensor products, while in characteristic 2 we completely classify irreducible tensor products where none of the modules appearing in the product is a basic spin module. In characteristic 2 we also give some necessary conditions for the tensor product of an irreducible module with a basic spin module to be irreducible.