Conjugacy classes in reductive groups and two-sided cells

TL;DR

This paper establishes a natural bijection between conjugacy classes of a connected reductive complex group and two-sided cells of a related algebra, providing new insights into the structure of such groups.

Contribution

It introduces a novel correspondence linking conjugacy classes in reductive groups to two-sided cells in an algebra, deepening understanding of their algebraic structure.

Findings

Bijection between conjugacy classes and two-sided cells

New structural insights into reductive groups

Connections between group theory and algebraic cells

Abstract

Let G' be a connected reductive group over the complex numbers. We show that the set of conjugacy classes of G' is in natural bijection with the set of two-sided cells associated to a certain algebra.