Mathematics Seminar Series: Algebra, Geometry, and Combinatorics

Speaker: Peter Tingley (Loyola University Chicago)

Title: Crystals and GL_n combinatorics

Abstract: This expository talk will give an introduction to crystals and crystal bases for finite dimensional representations of simple Lie algebras/groups. This will be done mainly with examples, focusing on the case of GL_n. We will discuss how these combinatorial structures arise from the representation theory, how they can be understood combinatorially, and how they can be used to understand things like tensor product multiplicities.