Endotrivial representations of finite groups and equivariant line bundles on the Brown complex

TL;DR

This paper explores the connection between endotrivial representations of finite groups in characteristic p and equivariant line bundles on the Brown complex, using weak homomorphisms to establish the relationship.

Contribution

It introduces a novel link between representation theory and equivariant topology via weak homomorphisms on the Brown complex.

Findings

Established a correspondence between endotrivial representations and equivariant line bundles.

Provided new insights into the structure of p-subgroups in finite groups.

Extended the understanding of equivariant line bundles in relation to group representations.

Abstract

We relate endotrivial representations of a finite group in characteristic p to equivariant line bundles on the simplicial complex of non-trivial p-subgroups, by means of weak homomorphisms.