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Let G be a finite group and let k be a field. Our purpose is to investigatethe simple modules for the double Burnside ring kB(G,G). It turns out that theyare evaluations at G of simple biset functors. For a fixed finite group H, weintroduce a suitable bilinear form on kB(G,H) and we prove that the quotient ofkB(-,H) by the radical of the bilinear form is a semi-simple functor. Thisallows for a description of the evaluation of simple functors, hence of simplemodules for the double Burnside ring.

Simple biset functors and double Burnside rings