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.
adler@uakron.edu
Alan Roche
Dept. of Mathematics, University of Oklahoma, Norman, OK 73019-0315, U.S.A.
aroche@math.ou.edu
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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