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Norm estimates for unitarizable highest weight modules

Bernhard Krötz — 1999

Annales de l'institut Fourier

We consider families of unitarizable highest weight modules ( ℋ λ ) λ ∈ L on a halfline L . All these modules can be realized as vector valued holomorphic functions on a bounded symmetric domain 𝒟 , and the polynomial functions form a dense subset of each module ℋ λ , λ ∈ L . In this paper we compare the norm of a fixed polynomial in two Hilbert spaces corresponding to two different parameters. As an application we obtain that for all λ ∈ L the module of hyperfunction vectors ℋ λ - ∞ can be realized as the space of all holomorphic...

Finite orbit decomposition of real flag manifolds

Bernhard Krötz;  Henrik Schlichtkrull — 2016

Journal of the European Mathematical Society

Let G be a connected real semi-simple Lie group and H a closed connected subgroup. Let P be a minimal parabolic subgroup of G . It is shown that H has an open orbit on the flag manifold G / P if and only if it has finitely many orbits on G / P . This confirms a conjecture by T. Matsuki.

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