Central morphisms and Cuspidal automorphic Representations

2018/12/07 by Labesse, Jean-Pierre, Schwermer, Joachim · 1 citation
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1812.03033

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→ 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 π of G(\mathbb A_F) its restriction to H(\mathbb A_F) contains a cuspidal representation σ of H(\mathbb A_F). Conversely, assuming moreover that f is an injection, any irreducible cuspidal representation σ of H(\mathbb A_F) appears in the restriction of some cuspidal representation π of G(\mathbb A_F). This theorem has an obvious local analogue.

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