Automorphisms and symplectic leaves of Calogero-Moser spaces

Cédric Bonnafé (1)

1 IMAG - Institut Montpelliérain Alexander Grothendieck

We study the symplectic leaves of the subvariety of fixed points of an automorphism of a Calogero-Moser space induced by an element of finite order of the normalizer of the associated complex reflection group. We give a parametrization à la Harish-Chandra of its symplectic leaves (generalizing earlier works of Bellamy and Losev). This result is inspired by the mysterious relations between the geometry of Calogero-Moser spaces and unipotent representations of finite reductive groups, which is the theme of another paper.

Domaines: Géométrie algébrique [math.AG]; Théorie des représentations [math.RT]

Cédric Bonnafé. Automorphisms and symplectic leaves of Calogero-Moser spaces. Journal of the Australian Mathematical Society, 2023, 115, pp.26-57. ⟨10.1017/S1446788722000180⟩. ⟨hal-03565121v2⟩