From the general linear group to graphs and beyond
by Carl Mautner
Abstract: The Schur algebra is a finite-dimensional algebra that encodes the rich representation theory of the general linear group. Motivated by geometry, Tom Braden and I have defined a similar algebra associated to any graph or, more generally, matroid. After introducing the various objects involved, I will discuss how our work `categorifies’ some combinatorial results about matroids and discuss some new combinatorial questions that it raises.