Weiqiang Wang (University of Virginia) & Ming Lu (Sichuan University)
The i-quantum groups arising from quantum symmetric pairs can be viewed as a natural generalization of Drinfeld-Jimbo quantum groups. Various fundamental constructions on quantum groups, including the q-Schur duality, R-matrix and canonical basis, have been generalized to i-quantum groups.
This mini-course addresses the Hall algebra realization of i-quantum groups recently developed by Ming Lu and Weiqiang Wang. This construction includes a reformulation of Bridgeland's Hall algebra realization for a whole quantum group. To that end, we introduce a class of finite-dimensional algebras called i-quiver algebras, and develop its representation theory. We shall also explain the i-divided powers, Serre presentation and braid group symmetries for i-quantum groups. Throughout, we shall focus on and work out various rank 1 and 2 examples.