Discrete Series Representations of Unipotent p-adic Groups

For a certain class of locally profinite groups, we show that an irreducible smooth discrete series representation is necessarily supercuspidal and, more strongly, can be obtained by induction from a linear character of a suitable open and compact modulo center subgroup.If F is a non-Archimedean local field, then our class of groups includes the groups of F -points of unipotent algebraic groups defined over F .We therefore recover earlier results of van Dijk and Corwin.