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arXiv · 2307.13742

Dirac cohomology and $\Theta$-correspondence for complex dual pairs

Spyridon Afentoulidis-Almpanis·Gang Liu·Salah Mehdi
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Abstract

We study the behavior of Dirac cohomology under Howe's $\Theta$-correspondence in the case of complex reductive dual pairs. More precisely, if $(G_1,G_2)$ is a complex reductive dual pair with $G_1$ and $G_2$ viewed as real groups, we describe those Harish-Chandra modules $\pi_1$ of $G_1$ with nonzero Dirac cohomology whose $\Theta$-liftings $\Theta(\pi_1)$ still have nonzero Dirac cohomology. In this case, we compute explicitly the Dirac cohomology of $\Theta(\pi_1)$.

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BibTeXRIS

Spyridon Afentoulidis-Almpanis, Gang Liu, Salah Mehdi. 2023-07-25. Dirac cohomology and $\Theta$-correspondence for complex dual pairs. https://arxiv.org/abs/2307.13742

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