Simple biset functors and double Burnside rings

Serge Bouc (1) , Radu Stancu (1) , Jacques Thévenaz (2)

1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352
2 Section de Mathematiques [Lausanne]

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.

Mots clés: biset; Burnside ring; simple module

Domaines: Théorie des groupes [math.GR]

Serge Bouc, Radu Stancu, Jacques Thévenaz. Simple biset functors and double Burnside rings. 2012. ⟨hal-00675555⟩