报告题目：Introduction to Kazhdan-Lusztig theory

报告人：谢迅 副教授（北京理工大学）

时间：2025.5.29 10:00-11:00

地点：数学大楼912

摘要：In 1979, Kazhdan and Lusztig introduced the Kazhdan-Lusztig basis of Hecke algebras, which has had a significant impact on the development of representation theory. This report will cover some concepts in this theory, including the a-function and the asymptotic ring. In collaboration with others, we have provided a combinatorial algorithm for the a-function of classical Weyl groups and applied it to the computation of the Gelfand-Kirillov dimension of the highest weight simple modules of semisimple Lie algebras. There have also been recent developments regarding Lusztig's conjecture on the structure of the asymptotic ring of affine Hecke algebras (which has been proven). Recently, we used the structure of asymptotic rings to prove that the number of left cells in the second-lowest two-sided cell is exactly half the number of elements in the Weyl group.

报告人简介：谢迅，北京理工大学数学与统计学院副教授。2015年博士毕业于中科院数学所。2017年入职北京理工大学。研究方向为李理论、表示论。研究工作涉及Kazhdan-Lusztig理论，李代数与Hecke代数，Coxeter群等。论文发表于《Int. Math. Res. Not.》《Adv. Math.》《Represent. Theory》《J. Algebra》等