Skip to main content
Skip to main menu Skip to spotlight region Skip to secondary region Skip to UGA region Skip to Tertiary region Skip to Quaternary region Skip to unit footer


Algebra Seminar: Weiqiang Wang (UVA)

Boyd Room 302

Title: Hall algebras and quantum symmetric pairs

Abstract: As a quantization of symmetric pairs, a quantum symmetric pair consists of a quantum group and its coideal subalgebra (called an i-quantum group). A quantum group can be viewed as an example of i-quantum groups associated to symmetric pairs of diagonal type. In recent years, several fundamental constructions (such as canonical bases, R-matrices) for quantum groups have been generalized to the setting of i-quantum groups. In this talk, we present a new Hall algebra construction of i-quantum groups. This relies on the framework of modified Ringel-Hall algebras of Lu-Peng. Our approach leads to monomial bases, PBW bases, and braid group actions for i-quantum groups. In case of symmetric pairs of diagonal type, our work reproduces of [Bridgeland2013]'s Hall algebra realization of a quantum group, which in turn was a generalization of earlier constructions of Ringel and Lusztig for half a quantum group. This is joint work with Min Lu (Sichuan University, China).

Support us

We appreciate your financial support. Your gift is important to us and helps support critical opportunities for students and faculty alike, including lectures, travel support, and any number of educational events that augment the classroom experience. Click here to learn more about giving.

Every dollar given has a direct impact upon our students and faculty.