Tuesday, May 5, 14:00, 7.527.

Carl Mautner (UC Riverside)
Schur algebras for matroids I, II.

Abstract:
In his 1901 thesis, Issai Schur discovered a finite dimensional algebra that connects the representation theory of the symmetric group and general linear group. Motivated by a geometric description the Schur algebra, Tom Braden and I discovered a family of Schur-like algebras associated to any matroid. Our original description of these algebras was frustratingly opaque. In this talk I will define a new, extended version of these matroidal Schur algebras with a simple presentation by generators and relations. Part I of the talk will explain my motivation and present an example, defined in terms of linear algebra over a finite field and related to the representation theory of GL(n,q). Part II of the talk will introduce the language of matroids and explain how the example from Part I generalizes to give a Schur-like algebra for any matroid.