Friday, February 10th, 2012
9:30am - 10:30am, in Campus Center 2-2545

Peter Tingley

MIT

Affine Mirkovic-Vilonen polytopes

Abstract: Kashiwara developed combinatorial objects called crystals to study the representation theory of complex simple Lie groups and Lie algebras. The construction is quite involved, but one can often realize the same combinatorics by more elementary means. I will explain one realization based on the Mirkovic-Vilonen polytopes of the title, and try to convince you it is useful. I will then explain current work giving an analogous construction for symmetric affine Kac-Moody algebras. This will be done mainly via examples and pictures, and I will not assume familiarity with the representation theory involved. This includes joint work with Pierre Baumann, Thomas Dunlap and Joel Kamnitzer.