Springer correspndence for complex reflection groups

TL;DR

This survey explores the Springer correspondence in relation to complex reflection groups, focusing on exotic symmetric spaces and the emergence of specific complex reflection groups in this context.

Contribution

It provides a comprehensive overview of the Springer correspondence for exotic symmetric spaces and highlights the natural appearance of certain complex reflection groups.

Findings

Complex reflection group $S_n times (z/rz)^n$ appears in exotic symmetric spaces.

The paper clarifies the Springer correspondence in the context of higher-level exotic symmetric spaces.

Abstract

This paper is a survey on the topics concerning the Springer correspondence related to the varieties such as the enhanced variety or the exotic symmetric space. We explain in the case of exotic symmetric space of higher level, the complex reflection group $S_n \ltimes (\BZ/r\BZ)^n$ appears naturally in the framework of the Springer correspondence.