"How Phases Appear When Reducing to
Quotient Groups, for Instance, as in Alperin's Conjecture"
By
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, November 18, 2013
Time: 13.40-14.30
Place: Mathematics Seminar Room,
SA-141
All are most cordially invited.
Tea and cookies will be served after the talk.