Geometric Representation Theory Seminar

Organizers：

Lin Chen, Will Donovan, Penghui Li, Peng Shan, Changjian Su, Wenbin Yan

Speaker：

Fan Qin 覃帆 (Beijing Normal University)

Time：

Fri., 15:30-16:30, May 30, 2025

Venue：

B626, Shuangqing Complex Building A

Title：

PBW type bases for quantum cluster algebras

Abstract:

Quantum cluster algebras associated with double Bott-Samelson cells have PBW type bases, which consist of monomials of fundamental variables. By extending them to the infinite rank setting, we recover the cluster structure on the virtual Grothendieck rings of representations of quantum affine algebras (i.e., derived Hall algebras). This allows us to compute the fundamental variables via braid group actions.