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Multiplicity bounds and the subrepresentation theorem for real spherical spaces


Authors: Bernhard Krötz and Henrik Schlichtkrull
Journal: Trans. Amer. Math. Soc. 368 (2016), 2749-2762
MSC (2010): Primary 22E45, 43A85
DOI: https://doi.org/10.1090/S0002-9947-2014-06427-1
Published electronically: November 24, 2014
MathSciNet review: 3449256
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Abstract: Let $ G$ be a real semi-simple Lie group and $ H$ a closed subgroup which admits an open orbit on the flag manifold of a minimal parabolic subgroup. Let $ V$ be a Harish-Chandra module. A uniform finite bound is given for the dimension of the space of $ H$-fixed distribution vectors for $ V$, and a related subrepresentation theorem is derived.


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Additional Information

Bernhard Krötz
Affiliation: Institut für Mathematik, Universität Paderborn, Warburger Straße 100, D-33098 Paderborn, Germany
Email: bkroetz@math.uni-paderborn.de

Henrik Schlichtkrull
Affiliation: Department of Mathematics, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen Ø, Denmark
Email: schlicht@math.ku.dk

DOI: https://doi.org/10.1090/S0002-9947-2014-06427-1
Keywords: Homogeneous space, Harish-Chandra module, subrepresentation theorem
Received by editor(s): September 4, 2013
Received by editor(s) in revised form: November 22, 2013, January 14, 2014, and March 8, 2014
Published electronically: November 24, 2014
Article copyright: © Copyright 2014 American Mathematical Society

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