Multiplicity bounds and the subrepresentation theorem for real spherical spaces

Bernhard Krötz, Henrik Schlichtkrull

Published 2013-09-04, updated 2014-03-15Version 2

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 sharp finite bound is given for the dimension of the space of H-fixed distribution vectors for V and a related subrepresentation theorem is derived. Extended final version. To appear in Trans. Amer. Math. Soc.