# Hall Algebras and Canonical Bases

## GAP Seminar

## Meeting Details

For more information about this meeting, contact Ping Xu, Nigel Higson, Mathieu Stiénon.

**Speaker:** Zongzhu Lin, Kansas State University

**Abstract:** Ringel described the Hall algebras of finite type
quiver via representations of the quivers over finite fields and
proved that the Hall algebra is isomorphism (with an certain
twisted) to the positive part of the quantized enveloping algebra
of the Lie algebra whose Dynkin diagram is the underlying graph
of the quiver. Lusztig used the geometric approach to Ringel's
construction and discovered a basis for the positive part of the
quantized enveloping algebra as the simple perverse sheaves over
classes of representation varieties. Such construction was
generalized to other quivers with out loops. In this talk I will
outline Lusztig's construction and various ways to describe the
canonical basis for affine quivers using representation theory
properties of the affine quivers.

## Room Reservation Information

**Room Number:** 106 McAllister

**Date:** 10/20/2009

**Time:** 2:30pm - 3:30pm