On local categories of finite groups II

Fei Xu

Published 2017-02-15Version 1

Local categories of a finite group $G$ are considered as generalized subquotient groups, and their representations contribute to group representations. To show this, we investigate the (stable) Grothendicek groups of the relevant local category algebras, as well as several natural maps among them. In this way, we may realize homology representations of $G$ via a generalized induction process. We also provide a new way to reformulate the Alvis-Curtis duality when $G$ is Chevalley.