Unipotent Representations Attached to the Principal Nilpotent Orbit

TL;DR

This paper constructs and classifies special unipotent representations of real reductive groups linked to the principal nilpotent orbit, providing formulas for their key properties.

Contribution

It introduces a comprehensive classification and explicit formulas for unipotent representations associated with the principal nilpotent orbit.

Findings

Formulas for K-types, associated varieties, and Langlands parameters.

Complete classification of special unipotent representations.

New insights into the structure of representations linked to the principal nilpotent orbit.

Abstract

In this paper, we construct and classify the special unipotent representations of a real reductive group attached to the principal nilpotent orbit. We give formulas for the $\mathbf{K}$-types, associated varieties, and Langlands parameters of all such representations.