Multiplicity bounds and the subrepresentation theorem for real spherical spaces (Q2787988)

Let \(G\) be a real semi-simple Lie group, \(P\) a minimal parabolic subgroup of \(G\) and \(H\) a closed subgroup of \(G\) such that there is an open \(P\)-orbit on \(G/H\). For a Harish-Chandra module \(V\) with smooth completion, the paper under review gives a uniform finite bound for the dimension of the space of \(H\)-fixed distribution vectors for \(V\) and derives a related subrepresentation theorem which describes \(V\) as a submodule of a certain induced module. The obtained bound is essentially sharp, the equality is obtained for generic irreducible representations in the case when \(H\) is the opposite parabolic subgroup of \(P\).