Hall Algebras and Canonical Bases
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
Time: 2:30pm - 3:30pm