Dirac cohomology and $\Theta$-correspondence for complex dual pairs
| Autor: | Afentoulidis-Almpanis, Spyridon, Liu, Gang, Mehdi, Salah |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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 $\Theta(\pi_1)$. Comment: 19 pages |
| Databáze: | arXiv |
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