Central morphisms and cuspidal automorphic representations

[摘要] 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 -> G such that the induced morphism H-der -> 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(A(F)) its restriction to H(A(F)) contains a cuspidal representation sigma of H(A(F)). Conversely, assuming moreover that f is an injection, any irreducible cuspidal representation sigma of H(A(F)) appears in the restriction of some cuspidal representation pi of G(A(F)). This theorem has an obvious local analogue. (C) 2019 Elsevier Inc. All rights reserved.

[发布日期] 2019-12-01

[关键词] Automorphic representations