calogero-moser空间的自同构与辛叶

Pub Date : 2021-12-23 DOI:10.1017/S1446788722000180

C'edric Bonnaf'e

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引用次数: 4

摘要

研究了由相关复反射群的正则化项的有限阶元素所导出的Calogero-Moser空间的自同构不动点的子簇的辛叶。我们给出了它的辛叶的参数化(概括了Bellamy和Losev的早期工作)。这个结果的灵感来自于Calogero-Moser空间的几何与有限约化群的单幂表示之间的神秘关系，这是另一篇论文的主题，C. bonnaf [' Calogero-Moser空间与单幂表示'，纯应用。数学。[j].， to appear，预印本，2021,arXiv:2112.13684]。

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AUTOMORPHISMS AND SYMPLECTIC LEAVES OF CALOGERO–MOSER SPACES

Abstract 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, C. Bonnafé [‘Calogero–Moser spaces vs unipotent representations’, Pure Appl. Math. Q., to appear, Preprint, 2021, arXiv:2112.13684].

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