报告人： 宋金峰 博士后

报告题目： Quantum Symmetric Pairs at Roots of Unity

时间： 2026年10月12日（周一）19:30—20:30

地点： 线上腾讯会议（会议号：885-887-630）

报告摘要：

Quantum symmetric pairs are distinguished coideal subalgebras of Drinfeld–Jimbo quantum groups that quantize symmetric pairs of Lie algebras. Their theory has flourished in recent years, with deep connections to canonical bases, representation theory, Poisson geometry, and braided module categories. However, their representation theory remains challenging, partly because they generally lack a natural triangular decomposition.

In this talk, I will explain how we extend the De Concini–Kac–Procesi theory to quantum symmetric pairs at roots of unity. We construct a Frobenius center and identify it with the coordinate algebra of a Poisson homogeneous space, connecting irreducible representations to the geometry of twisted conjugacy classes. We also describe the full center and determine the maximal dimension of irreducible representations. As an application, we construct a finite-dimensional coideal subalgebra of Lusztig’s small quantum group with an explicit PBW basis. This is joint work with Weinan Zhang (Shenzhen University).

报告人简介：

宋金峰，香港科技大学数学系博士后，合作导师为 Ivan Ip 教授。2025年获新加坡国立大学数学博士学位，师从鲍涣辰教授；2020年本科毕业于浙江大学数学系。主要研究方向为表示论、量子群及其与丛代数、泊松几何的交叉研究，尤其关注量子对称对、对称空间、典范基、单位根量子群及其几何与表示理论。已在 Cambridge Journal of Mathematics、Proceedings of the London Mathematical Society、Selecta Mathematica 等国际期刊发表论文。