On existence of generic cusp forms on semisimple algebraic groups

Moy, Allen; Muić, Goran

doi:10.1090/tran/7081

On existence of generic cusp forms on semisimple algebraic groups
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Trans. Amer. Math. Soc. 370 (2018), 4731-4757 Request permission

Abstract:

In this paper we discuss the existence of certain classes of cuspidal automorphic representations having non-zero Fourier coefficients for a general semisimple algebraic group $G$ defined over a number field $k$ such that its Archimedean group $G_\infty$ is not compact. When $G$ is quasi-split over $k$, we obtain a result on existence of generic cuspidal automorphic representations which generalize results of Vignéras, Henniart, and Shahidi. We also discuss: (i) the existence of cuspidal automorphic forms with non-zero Fourier coefficients for congruence of subgroups of $G_\infty$, and (ii) applications related to the work of Bushnell and Henniart on generalized Whittaker models.

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