Almost unramified discrete spectrum for split groups over Fq(t)

Abstract

Let G be a split adjoint group defined over F_q, let F_q(t), and let A be the adèles of F. We describe the local constituents at two points of automorphic representations of G in the discrete part of L²(G(F)\G(A)) which have vectors invariant under Iwahori subgroups at these two points and are unramified at all other points.