Simple biset functors and double Burnside ring

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.


Published in:
Journal of Pure and Applied Algebra, 217, 546-566
Year:
2013
Publisher:
Amsterdam, Elsevier
ISSN:
0022-4049
Keywords:
Laboratories:




 Record created 2012-04-26, last modified 2018-09-13

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