Multiplicity bounds and the subrepresentation theorem for real spherical spaces

Krötz, Bernhard; Schlichtkrull, Henrik

doi:10.1090/S0002-9947-2014-06427-1

Multiplicity bounds and the subrepresentation theorem for real spherical spaces
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Trans. Amer. Math. Soc. 368 (2016), 2749-2762 Request permission

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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