Speaker: 余世霖教授，华东师范大学

Inviter: 聂思安

Title: Geometry of special pieces and orbit method

Language: Chinese

Time & Venue: 2025.09.12 14:30-15:30 南楼N818

Abstract: I will report two ongoing work:The first one is joint work with Juteau, Levy and Sommers. We confirm the special pieces conjecture of Lusztig in all cases, which claims that the special piece associated to any special nilpotent orbit of a complex semisimple Lie algebra is the quotient of a smooth (symplectic variety) by a finite group action. The case of classical Lie algebras were previously obtained by Kraft-Procesi. Our proof is based on the previous work of Fu-Juteau-Levy-Sommers on the geometry of Slodowy slices of special pieces.The second work is by the speaker alone. I will exhibit an unexpected connection between the special pieces conjecture and unitarity of special unipotent representations of real linear reductive Lie groups in the sense of Arthur and Adams-Barbasch-Vogan. As a consequence, a uniform proof of unitarity of all special unipotent representations of all reductive groups is obtained, based on recent preprints of Adams-Mason-Brown-Vogan, Davis-Mason-Brown and my previous joint work with Conan Leung on orbit method. The case of classical groups was previously established by Barbasch-Ma-Sun-Zhu using Howe duality.