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