Journal of Lie Theory
Vol. 15, No. 1, pp. 261–267 (2005)
Discrete Series Representations of Unipotent $p$-adic Groups
Jeffrey D. Adler and Alan RocheJeffrey D. Adler
Department of Theoretical and Applied Mathematics
The University of Akron
Akron, OH 44325-4002
Department of Mathematics
University of Oklahoma
Norman, OK 73019-0315
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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