On Representations of Reductive pp--adic Groups over Q\mathbb Q--algebras

In this paper we study certain category of smooth modules for reductive $p$--adic groups analogous to the usual smooth complex representations but with the field of complex numbers replaced by a $\mathbb Q$--algebra. We prove some fundamental results in these settings, and as an example we give a classification of admissible unramified irreducible representations proving by reduction to the complex case that if the space of $K$--invariants is finite dimensional in an irreducible smooth unramified representation that the representation is admissible.Comment: In v.2 we updated references and the introductio

Some results on the Schwartz space of Γ G

Let G be a connected semisimple Lie group with finite center. Let Γ ⊂ G be a discrete subgroup. We study closed admissible irreducible subrepresentations of the space of distributions S(Γ G)\u27 defined by Casselman, and their relations to automorphic forms on Γ G when Γ is a congruence subgroup

Degenerate Eisenstein series on symplectic groups

In this paper we describe the generalization of usual notion of Siegel Eisenstein series (see for example [9]) to give a simple and natural construction of some classes of square--integrable automorphic representations for symplectic groups. The construction of automorphic representations obtained in this paper is an automorphic version of the local construction of strongly negative unramified representations [5] or of discrete series obtained by Tadić [11] in early 90\u27s (see also later work [8]). This is taken from our paper [7]. As an application we show how one can obtain an automorphic realization of certain global spherical representations. This has an interesting consequence locally and globally. We adopt Arthur\u27s point of view (see [2]