Simple biset functors and double Burnside rings
Group Theory
2012-03-02 v1
Abstract
Let G be a finite group and let k be a field. Our purpose is to investigate the simple modules for the double Burnside ring kB(G,G). It turns out that they are evaluations at G of simple biset functors. For a fixed finite group H, we introduce a suitable bilinear form on kB(G,H) and we prove that the quotient of kB(-,H) by the radical of the bilinear form is a semi-simple functor. This allows for a description of the evaluation of simple functors, hence of simple modules for the double Burnside ring.
Keywords
Cite
@article{arxiv.1203.0195,
title = {Simple biset functors and double Burnside rings},
author = {Serge Bouc and Radu Stancu and Jacques Thévenaz},
journal= {arXiv preprint arXiv:1203.0195},
year = {2012}
}