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Journal Article

#### Central morphisms and cuspidal automorphic representations

##### External Resource

https://doi.org/10.1016/j.jnt.2019.05.005

(Publisher version)

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##### Fulltext (public)

arXiv:1812.03033.pdf

(Preprint), 286KB

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##### Citation

Labesse, J.-P., & Schwermer, J. (2019). Central morphisms and cuspidal automorphic
representations.* Journal of Number Theory,* *205*, 170-193.
doi:10.1016/j.jnt.2019.05.005.

Cite as: https://hdl.handle.net/21.11116/0000-0004-9A5B-9

##### Abstract

Let $F$ be a global field. Let $G$ and $H$ be two connected reductive group defined over $F$ endowed with an $F$-morphism $f: H\rightarrow G$ such that the induced morphism $H_{der}\rightarrow G_{der}$ on the derived groups is a central isogeny. Our main results yield in particular the following theorem: Given any irreducible cuspidal representation $\pi$ of $G(\mathbb A_F)$ its

restriction to $H(\mathbb A_F)$ contains a cuspidal representation $\sigma$ of

$H(\mathbb A_F)$. Conversely, assuming moreover that $f$ is an injection, any

irreducible cuspidal representation $\sigma$ of $H(\mathbb A_F)$ appears in the restriction of some cuspidal representation $\pi$ of $G(\mathbb A_F)$. This theorem has an obvious local analogue.

restriction to $H(\mathbb A_F)$ contains a cuspidal representation $\sigma$ of

$H(\mathbb A_F)$. Conversely, assuming moreover that $f$ is an injection, any

irreducible cuspidal representation $\sigma$ of $H(\mathbb A_F)$ appears in the restriction of some cuspidal representation $\pi$ of $G(\mathbb A_F)$. This theorem has an obvious local analogue.