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Algebra Seminar: Weiqiang Wang (UVA)

Date and time:
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).

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