Shifted functors of linear representations are semisimple

TL;DR

This paper proves that the category of modules over shifted Green biset functors associated with finite groups over fields of characteristic zero is semisimple, extending understanding of their algebraic structure.

Contribution

It establishes the semisimplicity of module categories over shifted Green biset functors for finite groups over characteristic zero fields, a new result in representation theory.

Findings

Module categories over shifted Green biset functors are semisimple.

Semisimplicity holds for any finite group T over fields of characteristic zero.

The result generalizes previous knowledge about Green biset functors.

Abstract

We prove that, for any fields $k$ and $\mathbb{F}$ of characteristic $0$ and any finite group $T$, the category of modules over the shifted Green biset functor $(kR_{\mathbb{F}})_T$ is semisimple.