On existence of generic cusp forms on semisimple algebraic groups

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_∞ 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_∞, and (ii) applications related to the work of Bushnell and Henniart on generalized Whittaker models.