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.