On the coordinate ring of spherical conjugacy classes

TL;DR

This paper investigates the structure of the coordinate ring of spherical conjugacy classes in simple algebraic groups, providing a detailed decomposition into simple modules.

Contribution

It explicitly determines the decomposition of the coordinate ring of spherical conjugacy classes into simple G-modules, a novel result in the representation theory of algebraic groups.

Findings

Explicit decomposition of coordinate rings into simple modules

Identification of the structure of spherical conjugacy classes

Advancement in understanding algebraic group representations

Abstract

Let G be a simple algebraic group over an algebraically closed field of characteristic zero and X be a spherical conjugacy class of G. We determine the decomposition of the coordinate ring of X into simple G-modules.