Speaker
Dr
Radu Stancu
(LAMFA, Université de Picardie)
Description
This is a joint work with Serge Bouc and Jacques Thévenaz.
Let G be a finite group and k be a field. The purpose of this talk is to investigate the simple modules for the double Burnside ring kB(G;G).
It turns out that these modules 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 prove that the quotient of the functor kB(-;H) by the radical of the bilinear form is semi-simple. This allows for a description of the evaluation of simple functors, hence of simple modules for the double Burnside ring.
The evaluation of a simple biset functor at a finite group G may be zero. We give examples where this happens, as well as where this does not occur. Under some restrictive conditions on G we can give a closed formula for such an evaluation.
| Mots Clés / Keywords | double Burnside ring, simple biset fuctors |
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Primary author
Dr
Radu Stancu
(LAMFA, Université de Picardie)
