Discrete Series Representations of Unipotent $p$-adic Groups

Jeffrey D. Adler and Alan Roche

Abstract: 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.

Keywords: $p$-adic group, locally profinite group, nilpotent group, discrete series, supercuspidal representation

Classification (MSC2000): 22E50, 20G05, 22E27

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