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Journal of Lie Theory 15 (2005), No. 1, 261--267
Copyright Heldermann Verlag 2005

Discrete Series Representations of Unipotent p-adic Groups

Jeffrey D. Adler
Dept. of Theoretical and Applied Mathematics, University of Akron, Akron, OH 44325-4002, U.S.A.

Alan Roche
Dept. of Mathematics, University of Oklahoma, Norman, OK 73019-0315, U.S.A.

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.

MSC: 22E50; 20G05, 22E27

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