Dirac series of $E_{7(-25)}$

TL;DR

This paper classifies all irreducible unitary representations with non-zero Dirac cohomology for the Hermitian symmetric real form E_{7(-25)}, refining previous bounds to achieve a complete classification.

Contribution

It provides a complete classification of certain unitary representations of E_{7(-25)} by sharpening the Helgason-Johnson bound, advancing understanding of Dirac cohomology in this context.

Findings

Complete classification of irreducible unitary representations with non-zero Dirac cohomology for E_{7(-25)}

Refinement of the Helgason-Johnson bound for this classification

Enhanced understanding of the structure of representations of E_{7(-25))

Abstract

By further sharpening the Helgason-Johnson bound in 1969, this paper classifies all the irreducible unitary representations with non-zero Dirac cohomology of the Hermitian symmetric real form $E_{7(-25)}$.