Geometric Representation Theory Seminar
Organizers：
Lin Chen, Will Donovan, Penghui Li, Peng Shan, Changjian Su, Wenbin Yan
Speaker：
Cédric Bonnafé (CNRS, Université Montpellier)
Time：
Wed., 15:30-16:30
Oct. 23, 2024
Venue：
Ning Zhai (新宁斋) 101
Title：
Calogero-Moser spaces vs unipotent representations
Abstract：
Lusztig's classification of unipotent representations of finite reductive groups depends only on the associated Weyl group W (endowed with its Frobenius automorphism). All the structural questions (families, Harish-Chandra series, partition into blocks...) have an answer in a combinatorics that can be entirely built directly from W . Over the years, we have noticed that the same combinatorics seems to be encoded in the Poisson geometry of a Calogero-Moser space associated with W (roughly speaking, families correspond to ${\mathbb{C}}^\times$-fixed points, Harish-Chandra series correspond to symplectic leaves, blocks correspond to symplectic leaves in the fixed point subvariety under the action of a root of unity). The aim of this talk is to gather these observations, state precise conjectures and provide general facts and examples supporting these conjectures.
