Cluster algebra realization of quantum groups and their positive representations

Date: 
2018/02/16 Fri 15:45 - 16:45
Room: 
Room 402, RIMS
Speaker: 
Gus Schrader
Affiliation: 
Columbia University
Abstract: 

I will speak about recent joint work with Alexander Shapiro in which we develop a cluster realization of the quantum group U_q(sl(n)) using quantized moduli spaces of framed local systems on marked surfaces. I will also discuss the notion of a positive representation of a quantum cluster algebra, and explain how the positive representations of U_q(sl(n)) introduced by Frenkel and Ip can be studied in the cluster algebra framework.