Special Session 109: Cluster Algebras, Hall Algebras and Their Applications

Exceptional curves and quantum loop algebras
Ming Lu
Sichuan University
Peoples Rep of China
Co-Author(s):    Zhongwei Fang, Shiquan Ruan
Abstract:
Schiffmann and Dou-Jiang-Xiao use the Hall algebras of weighted projective lines to realize quantum loop algebras of simply-laced type. In this talk, we generalize their results, and use the Hall algebras of exceptional curves to realize the quantum loop algebras associated to the corresponding valued star-shaped graphs. In particular, we are able to realize (twisted and untwisted) quantum affine algebras in Drinfeld new presentation.