Some small unipotent representations of indefinite orthogonal groups

We study a family of small unitary representations of indefinite orthogonal groups. These representations arise as analytic continuations of the discrete series and were studied extensively by Knapp in [K3]. We complete Knapp's analysis by proving that they are irreducible. In order to do so we...

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Bibliographic Details
Published in:Journal of functional analysis 2004-08, Vol.213 (2), p.290-320
Main Author: Trapa, Peter E
Format: Article
Language:English
Subjects:
Orbit method
Singular unitary representations
Unipotent representations
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Summary:We study a family of small unitary representations of indefinite orthogonal groups. These representations arise as analytic continuations of the discrete series and were studied extensively by Knapp in [K3]. We complete Knapp's analysis by proving that they are irreducible. In order to do so we prove that the representations are unipotent and have irreducible associated cycles in which all multiplicities are exactly one. Moreover, we prove that the K-type structure of each representation matches (up to a shift) the K-type structure of the ring of functions on the closure a nilpotent K C orbit on p .
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2003.09.003