Dirac cohomology of minimal representations

TL;DR

This paper investigates the Dirac cohomology of minimal representations across all real reductive groups, providing new insights and counterexamples related to existing conjectures, especially in equal rank cases.

Contribution

It offers a comprehensive analysis of Dirac cohomology for minimal representations and challenges a previous conjecture in the equal rank setting.

Findings

Counterexamples to Huang's conjecture in equal rank cases

Complete characterization of Dirac indices for minimal representations

New theoretical insights into the structure of real reductive groups

Abstract

In this paper, we study the Dirac cohomology of minimal representations for all real reductive groups G. The Dirac indices of these representations are also studied when G is of equal rank, giving some counterexamples of a conjecture of Huang proposed in 2015.