Regular functions on covers of nilpotent coadjoint orbits

TL;DR

This paper investigates the connection between regular functions on nilpotent orbit covers and unipotent representations, enhancing understanding of their algebraic and geometric structures in complex groups.

Contribution

It introduces a novel link between regular functions on covers of nilpotent orbits and unipotent representations, providing new insights into their interplay.

Findings

Established a correspondence between regular functions and unipotent representations.

Clarified the structure of regular functions on nilpotent orbit covers.

Enhanced the understanding of the geometric aspects of unipotent representations.

Abstract

In this paper I explore the relationship between regular functions associated to local systems on nilpotent orbits and unipotent representations in the complex groups.