Student Combinatorics Seminar Seminar

The representation theory of GL(n) is very well understood in characteristic 0. Associated to each partition of length at most n, there is an irreducible representation of GL(n). There are several functorial ways to construct the irreducible representations. In positive characteristic, each of these constructions will still yield a representation of GL(n). However, they will not in general be irreducible, nor will the different constructions agree. We will consider the Schur module construction. In trying to prove a version in positive characteristic of the famous theorem of Weyl on polarization, we will run into an interesting combinatorial question on Schur modules. I expect that there should be more applications to this result. This is joint work with Derksen. Speaker(s): Viswambhara Makam (University of Michigan)