数学科学学院学术报告[2024] 113号
(高水平大学建设系列报告993号)
报告题目: Dual canonical basis of quantum group
报告人:卢明 教授(四川大学)
报告时间:2024年11月8日上午15:30-16:30
讲座地点:汇文楼1420
报告内容:There are two important ways to realize quantum groups, one is Hall algebra given by Ringel and Bridgeland, the other is convolution algebra of perverse sheaves given by Lusztig, Nakajima and Qin. In this talk, we shall compare these two realizations. The perverse sheaves give the dual canonical bases of quantum groups by Hernandez-Leclerc and Qin. We construct the dual canonical bases via Hall algebras, and prove that the transition matrix from the dual canonical basis to the basis of Hall algebras is integral and positive, which extend Lusztig’s result. We further prove the dual canonical basis coincides with the double canonical basis defined by Bernstein-Greenstein, and solve some Bernstein-Greenstein’s conjectures. This is joint work with Xiaolong Pan.
报告人简历:卢明,四川大学教授,国家人才计划(青年学者),研究兴趣为代数表示论与李理论。目前主要从事量子群和i-量子群的Hall代数实现和几何实现的研究,在Proc. London Math. Soc, Adv. Math, Comm. Math.Phys., Selecta Math., Trans. AMS等数学杂志上发表40余篇论文。
欢迎师生参加!
邀请人:方颖珏
数学科学学院
2024年月11月6日