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Hall algebras and i-quantum groups

Prof. Weiqiang Wang(美国弗吉尼亚大学)
Thursday, March 14th, 2019, 1:30 PM  闵行数学楼126室
王伟强教授任职于美国弗吉尼亚大学数学系,是国际上极具影响力的表示论研究专家。他的重要工作发表在《Inv. Math.》, 《Duke Math. J.》等诸多数学顶级杂志上,总被引次数过千。他还著有Graduate Studies in Mathematics系列第144卷 《Dualities and representations of Lie superalgebras》。同时王伟强教授还担任国际一流数学期刊 《Int. Math. Res. Not.》 的编委。

A quantum symmetric pair consists of a quantum group and its coideal subalgebra (called an i-quantum group). Quantum groups can be viewed as an example of i-quantum groups associated to symmetric pairs of diagonal type. In recent years, many fundamental constructions for quantum groups have been generalized to the i-quantum group setting. In this talk, we present a categorification of i-quantum groups via a new Hall algebra approach. This relies on the framework of modified Ringel-Hall algebras of Ming Lu and Liangang 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 reduces to a reformulation of Bridgeland'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).

主持人: 罗栗
主办单位:数学科学学院 科技处
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