Unitary representations with Dirac cohomology: finiteness in the real case

Abstract

Let $G$ be a complex connected simple algebraic group with a fixed real form $\sigma$. Let $G(\mathbb{R})=G^{\sigma }$ be the corresponding group of real points. This paper reports a finiteness theorem for the classification of irreducible unitary Harish-Chandra modules of $G(\mathbb{R})$ (up to equivalence) having non-vanishing Dirac cohomology. Moreover, we study the distribution of the spin norm along Vogan pencils for certain $G(\mathbb{R})$, with particular attention paid to the unitarily small convex hull introduced by Salamanca-Riba and Vogan.

Further extended version, 31 pages

References in corpus (2)

• Unitary Representations with Dirac cohomology: a finiteness result for complex Lie groups
• Unitary Representations with non-zero Dirac cohomology for complex $E_6$

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