讲座题目：Dirac series and coherent continuation in orbit method 主讲人：Prof. Jingsong Huang 主持人：舒斌 教授 开始时间：2019-07-10 14:00:00 结束时间：2019-07-10 15:00:00 讲座地址：数学楼102室 主办单位：数学科学学院
报告人简介： 黄劲松，香港科技大学讲席教授。1984年本科毕业于北京大学，1989年研究生毕业于麻省理工学院获博士学位。后陆续在美国普林斯顿高等研究所从事研究；在美国盐湖城大学任教。1993年进入香港科技大学，2002年香港科技大学任教授。他的研究领域是表示论、李群上的非交换调和分析，尤其在Dirac算子、奇异酉表示等课题的研究上取得成就。 报告内容： Classifying irreducible unitary representations of real reductive Lie groups is a central problem in representation theory, which is well-known as the unitary dual problem. The orbit method establishes a correspondence between irreducible unitary representations of a Lie group and its coadjoint orbits. Diximer's work on primitive ideals gave one of the earliest indications of such a correspondence. The theory was established by Kirillov for nilpotent groups and it was later extended by Kostant and Auslander to solvable groups. Vogan proposed that the orbit method should serve as a unifying principle in the description of the unitary dual of real reductive groups. In Vogan's formulation of the orbit method for real reductive groups, the correspondence from the coadjoint orbits to irreducible unitary representations is divided into three steps according to the Jordan decomposition of a linear functional on Lie algebras into hyperbolic, elliptic and nilpotent components. The hyperbolic step and elliptic step are well understood, while the nilpotent step to construct unipotent representations from nilpotent orbits has been a focus of active research in many related areas. The aim of this talk is to show that our recent work joint with Pandzic and Vogan on classifying unitary representations by their Dirac cohomology shed light on understanding unipotent representations. In particular, the coherent continuation relates the Dirac series (irreducible unitary representations with nonzero Dirac cohomology) to unipotent representations. |
