"How Phases Appear When Reducing to Quotient Groups, for Instance, as in Alperin's Conjecture"
Abstract: This talk is a pedagogical introduction.Clifford theory reduces to quotient groups, but with the introduction of a twist: a phase factor, a cohomology class. Alperin's Conjecture says that the number of simples of a block is "locally determined" in terms of subquotients N(P)/P for p-subgroups P. After Puig, "locally determined" means determined by the fusion system up to finite information. But the fusion system, a category consisting of conjugation homomorphisms between p-subgroups, cannot see the subquotients PC(P)/P. To express Alperin's Conjecture in a truly local way, Clifford theory is applied to quotient out PC(P)/P from N(P,e)/P, where e is a suitable block of PC(P). The extra information in the introduced twists is finite.
Date: Monday, December 2, 2013
Place: Mathematics Seminar Room, SA-141
All are most cordially invited.
Tea and cookies will be served after the talk.