Dirac series for $E_{6(-14)}$

Abstract

Up to equivalence, this paper classifies all the irreducible unitary representations with non-zero Dirac cohomology for the simple Lie group $E_{6(-14)}$, which is of Hermitian symmetric type. Each FS-scattered Dirac series of $E_{6(-14)}$ is realized as a composition factor of certain $A_{\mathfrak{q}}(\lambda )$ module. Along the way, we have also obtained all the fully supported irreducible unitary representations of $E_{6(-14)}$ with integral infinitesimal characters.

32 pages, some strings are folded

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Cited by in corpus (7)

• A non-vanishing criterion for Dirac cohomology
• Dirac series of $E_{7(-5)}$
• Dirac series of $E_{7(-25)}$
• Dirac series of $E_{7(7)}$
• Vogan's FPP conjecture for complex Lie groups
• Dirac series of $E_{8(-24)}$
• Dirac cohomology, branching laws and Wallach modules