EVENT DETAILS AND ABSTRACT

Title: Kashiwara's crystals for affine Lie algebras
Speaker: Peter Tingley
Speaker Info: Loyola University
Brief Description:
Special Note:
Abstract:

I will introduce Kashiwara's crystals, particularly those related to affine Kac-Moody algebras. Crystals come from the theory of quantum groups, but they can often be constructed using elementary methods, giving a combinatorial approach to the representation theory of the corresponding Lie algebras. There are actually a number of different-seeming constructions, and I have for years been interesting in understanding the relationships between them. My current favorite way to do that is through the geometry of quiver varieties, so I'll tell you a bit about that as well. Much of the talk will be expository, although I'll touch on some of my own work (with various coauthors).