Simple modules over Green biset functors

TL;DR

This paper explores the classification of simple modules over Green biset functors, providing examples, supporting a conjecture, and proving it under specific conditions, advancing the understanding of biset functor representations.

Contribution

It offers three examples of Green biset functors with parametrized simple modules and proves Bouc's conjecture under certain hypotheses.

Findings

Three examples of Green biset functors with parametrized simple modules

Support and partial proof of Bouc's conjecture on simple modules

Advancement in classifying simple modules over Green biset functors

Abstract

We present three examples of Green biset functors for which their simple modules can be parametrized. These are particular cases of a conjecture by Serge Bouc classifying the simple modules over a Green biset functor A, that generalizes the classification of simple biset functors. We also prove this conjecture under certain hypothesis for A.