Blocks of the Grothendieck Ring of Equivariant Bundles on a Finite Group

Cédric Bonnafé

doi:10.53733/29

Authors

Cédric Bonnafé Universite Montpellier 2

DOI:

https://doi.org/10.53733/29

Keywords:

Grothendieck group, G-equivariant C-vector bundles

Abstract

If G is a finite group, the Grothendieck group $\mathbf{K}_G(G)$ of the category of G-equivariant $\mathbb{C}$ -vector bundles on G (for the action of G on itself by conjugation) is endowed with a structure of (commutative) ring. If K is a sufficiently large extension of $\mathbb{Q}_{\! p}$ and $\mathcal{O}$ denotes the integral closure of $\mathbb{Z}_{\! p}$ in K, the K-algebra $K\mathbf{K}_G(G)=K \otimes_\mathbb{Z} \mathbf{K}_G(G)$ is split semisimple. The aim of this paper is to describe the $\mathcal{O}$ -blocks of the $\mathcal{O}$ -algebra $\mathcal{O}\mathbf{K}_G(G)$ .