Department of Mathematics
"On some of the simple composition factors of the biset functor of p-permutation modules"
Abstract: A biset category C over an algebraically closed characteristic zero field K is a category whose set of objects is a suitable set of finite groups and the morphisms from G to H are the R-linear combinations of the isomorphism classes of sets with a left action of G and a right action of H. A biset functor on C is a K-linear functor from C to the category of vector spaces over K. Serge Bouc showed that, in the category of biset functors, the simple objects are the biset functors S(G,V) parametrized by pairs (G,V) up to an equivalence condition, where G is a group in C and V is a simple module of the group ring of Out(G) over K.
In this talk, we shall investigate the composition structure of the biset functor Kpp of p-permutation modules of p-modular group algebras. Maxime Ducellier(2015) gave a coarser description of the structure of Kpp, as a functor on a different category. His parametrization of simple functors involved parametrization of simple factors involved certain semidirect products H of a cyclic group over a p-group. Melanie Baumann (2012) conjectured that, given such H, then S(H,V) is a simple composition factor of Kpp as a biset functor if and only if V is the trivial module. In refutation of that conjecture, we shall give a weaker condition on V that is sufficient for S(H,V) to appear by obtaining structural information about Ducellier's simple objects.
Date: Monday, April 18, 2016
Place: Mathematics Seminar Room, SA-141
All are most cordially invited.Tea and cookies: before the seminar