广州数学大讲坛第六期

第五十五讲—华东师范大学余世霖教授学术报告

题目：Coadjoint orbit method and unitarity of special unipotent representations

时间：11月16日（周一）上午9:00

地点：腾讯会议（会议ID: 695-472-834)

报告人：余世霖 教授

摘要：Following the coadjoint orbit method philosophy, I will present a uniform construction of special unipotent representations of real forms of any complex simple group attached to a distinguished nilpotent orbit in the Langlands dual group, using deformation quantization. Consequently, all such representations have irreducible associated cycles and are therefore unitary by the theory of mixed Hodge modules. The case of real classical groups was previously established in the work of Barbasch, Ma, Sun and Zhu.

A key geometric ingredient in our construction is Lusztig's conjecture on the geometry of special pieces, which was proven for classical groups by Kraft and Procesi, and for the general case in my recent joint work with Juteau, Levy, and Sommers. The unitarity of general Arthur/Adams-Barbasch-Vogan packets can then be reduced to the distinguished case by the recent work of Adams, Ionov, Mason-Brown, and Vogan. This fully solves the unitary conjecture proposed by Arthur and Adams-Barbasch-Vogan about 40 years ago.

报告人简介：

余世霖，华东师范大学数学科学学院教授、博士生导师。主要从事非交换几何和李群表示论方面的研究。2007年本科毕业于复旦大学；2013年博士毕业于美国宾夕法尼亚州立大学（Pennsylvania State University）；2013-2019年分别在美国宾夕法尼亚大学（University of Pennsylvania）、香港中文大学、美国德克萨斯农工大学（Texas A&M University）从事博士后研究。2019年入职厦门大学，入选国家高层次青年人才计划。2024年入职华东师范大学。研究成果发表在Duke Math. J.，Math. Ann.，Adv. Math. 等国际高水平数学期刊。