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research article
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.
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Name
BST-simple-double-revised.pdf
Type
Preprint
Access type
openaccess
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428.55 KB
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Adobe PDF
Checksum (MD5)
2999d31be895202f90d3a8e1a4d3ce63