Hall algebras and quantum symmetric pairs III: Quiver varieties

The iota quiver algebras were introduced recently by the authors to provide a Hall algebra realization of universal iota quantum groups, which is a generalization of Bridgeland's Hall algebra construction for (Drinfeld doubles of) quantum groups; here an iota quantum group and a corresponding Drinfeld-Jimbo quantum group form a quantum symmetric pair. In this paper, the Dynkin miniver algebras are shown to arise as new examples of singular Nakajima-Keller-Scherotzke categories. Then we provide a geometric construction of the universal iota quantum groups and their dual canonical bases with positivity, via the quantum Grothendieck rings of Nakajima-Keller-Scherotzke quiver varieties, generalizing Qin's geometric realization of quantum groups of type ADE. (C) 2021 Elsevier Inc. All rights reserved.

Automated summary

The paper explores the applications of iota quiver algebras and Dynkin miniver algebras in the Nakajima-Keller-Scherotzke categories, and provides a geometric construction of universal iota quantum groups for quantum symmetric pairs.