Blocks of the Grothendieck ring of equivariant bundles on a finite group

Cédric Bonnafé (1)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier

If $G$ is a finite group, the Grothendieck group $\Kb_G(G)$ of the category of $G$-equivariant $\CM$-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 $\QM_{\! p}$ and $\OC$ denotes the integral closure of $\ZM_{\! p}$ in $K$, the $K$-algebra $K\Kb_G(G)=K \otimes_\ZM \Kb_G(G)$ is split semisimple. The aim of this paper is to describe the $\OC$-blocks of the $\OC$-algebra $\OC \Kb_G(G)$.

Mots clés: Equivariant bundles; Finite groups; blocks; Brauer map

Domaines: Théorie des représentations [math.RT]; Théorie des groupes [math.GR]

Cédric Bonnafé. Blocks of the Grothendieck ring of equivariant bundles on a finite group. 2014. ⟨hal-00995158v1⟩