Dirac series for complex $E_7$

TL;DR

This paper classifies the Dirac series for complex E7, verifying several longstanding conjectures and aiding the understanding of its unitary dual, thus advancing the representation theory of this exceptional Lie group.

Contribution

It provides the first complete classification of Dirac series for complex E7, confirming multiple conjectures and offering insights into the group's unitary dual.

Findings

Verification of conjectures from 2011, 2019, 2020

Complete classification of Dirac series for complex E7

Enhanced understanding of the unitary dual of complex E7

Abstract

This paper classifies the Dirac series for complex $E_7$. As applications, we verify a few conjectures raised in 2011, 2019 and 2020 for this exceptional Lie group. In particular, according to Conjecture 1.1 of Barbasch and Pandzic [BP], our classification should be helpful for understanding the unitary dual of complex $E_7$.