Special Colloquium
Julia Pevtsova
University of Washington
Modular Representation Theory and Cohomology: An Elementary Approach
Abstract: Modular representation theory studies actions of finite groups (Lie algebras, algebraic groups, finite group schemes) on vector spaces
over a field of positive characteristic. The simplest example is an action
of the cyclic group Z/p on a vector space. Such an action is described
by a single matrix which, in turn, is classified by its Jordan canonical
form. I shall describe an approach to the study of modular representations via
their restrictions to certain elementary subalgebras which are analogs of
one-parameter subgroups. As an application, we can recover the algebraic
variety associated to the cohomology ring of a finite group scheme G by
purely representation-theoretic means, in particular generalizing Quillen's
``stratification theorem" for group cohomology. As another application, we
construct new numerical invariants of representations. These invariants are
expressed in terms of Jordan forms. Most of our results apply to any finite group scheme, but they are
non-trivial even in the case of the finite group Z/p x Z/p, which is a
baby example that will be used for illustrative purposes throughout the
talk.
There will be a meet and greet right after the talk in SEO 300. Coffee, tea, & cookies will be provided.
Wednesday January 23, 2008 at 3:00 PM in SEO 636