Publication

Simple biset functors and double Burnside ring

Jacques Thévenaz
2013
Journal Articles

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.

Official source

https://infoscience.epfl.ch/entities/publication/76adcda5-2a15-43ff-a5f1-7f7c20596f1a

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Simple biset functors and double Burnside ring

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