## Crystals Learning Seminar

In this seminar we will learn about crystals, which are nice combinatorial models for representations of Lie algebras. The first half of the seminar will focus on quantum groups and construction of crystal bases from this perspective (Kashiwara's "grand loop argument"). The second half will focus on combinatorial (Young tableaux, Littelmann path model) and geometric (quiver varieties, MV polytopes) constructions.

### Introduction to quantum groups II

by Iva Halacheva | University of Toronto
Time: 15:00 — 16:30  (Monday, Sep. 26, 2011)
Location: BA6180, Bahen Center, 40 St. George St.
Abstract:
Let $g$ be a Kac-Moody algebra and $q\in\mathbb{C}$ not a root of unity. We introduce the category $\mathcal O^q_{\mathrm{int}}$ of integrable representations for the quantum group $U_q(g)$, and describe how it is a deformation of the category of integrable representations of $g$, in the sense that the latter is obtained as the "classical limit" $q\to 1$ of the former.

#### Dates in this series

· Monday, Sep. 26, 2011: Introduction to quantum groups II (Iva Halacheva)
· Monday, Nov. 21, 2011: The affine Grassmannian and geometric Satake correspondence (Brad Hannigan-Daley)
· Monday, Nov. 28, 2011: Crystals via Mirković-Vilonen cycles (Brad Hannigan-Daley)
· Monday, Dec. 05, 2011: MV polytope model for crystals (Joel Kamnitzer)