20 citations · 116 across the 20 of their papers we have counts for
27 papers
A note on -factorizations of representations
Pritam Ganguly, Bernhard Krötz, Job J. Kuit
In this paper we give an overview on -factorizations of Lie group representations and introduce the notion of smooth -factorization.
Poisson transform and unipotent complex geometry
Heiko Gimperlein, Bernhard Krötz, Luz Roncal +1
Our concern is with Riemannian symmetric spaces of the non-compact type and more precisely with the Poisson transform which maps generalized functions on th…
A Paley-Wiener theorem for Harish-Chandra modules
Heiko Gimperlein, Bernhard Krötz, Job J. Kuit +1
We formulate and prove a Paley-Wiener theorem for Harish-Chandra modules for a real reductive group. As a corollary we obtain a new and elementary proof of the Helgason conjecture.
Ellipticity and discrete series
Bernhard Krötz, Job J. Kuit, Eric M. Opdam +1
We explain by elementary means why the existence of a discrete series representation of a real reductive group implies the existence of a compact Cartan subgroup of . The pr…
Plancherel theory for real spherical spaces: Construction of the Bernstein morphisms
Patrick Delorme, Friedrich Knop, Bernhard Krötz +1
Given a unimodular real spherical space we construct for each boundary degeneration of a Bernstein morphism . We show t…
The infinitesimal characters of discrete series for real spherical spaces
Bernhard Krötz, Job J. Kuit, Eric M. Opdam +1
Let be the homogeneous space of a real reductive group and a unimodular real spherical subgroup, and consider the regular representation of on . It is shown tha…
Geometric counting on wavefront real spherical spaces
Bernhard Krötz, Eitan Sayag, Henrik Schlichtkrull
We provide -versus -bounds for eigenfunctions on a real spherical space of wavefront type. It is shown that these bounds imply a non-trivial error term estimate…
The constant term of tempered functions on a real spherical space
Raphaël Beuzart-Plessis, Patrick Delorme, Bernhard Krötz +1
Let be a unimodular real spherical space. We develop a theory of constant terms for tempered functions on which parallels the work of Harish-Chandra. The constant terms $f_…
Harmonic analysis for real spherical spaces
Bernhard Krötz, Henrik Schlichtkrull
We give an introduction to basic harmonic analysis and representation theory for homogeneous spaces attached to a real reductive Lie group . A special emphasis is made t…
Classification of reductive real spherical pairs I. The simple case
Friedrich Knop, Bernhard Krötz, Tobias Pecher +1
This paper gives a classification of all pairs with a simple real Lie algebra and a reductive subalgebra for…
Reductive group actions
Friedrich Knop, Bernhard Krötz
In this paper, we study rationality properties of reductive group actions which are defined over an arbitrary field of characteristic zero. Thereby, we unify Luna's theory of spher…
The tempered spectrum of a real spherical space
Friedrich Knop, Bernhard Krötz, Henrik Schlichtkrull
Let G/H be a unimodular real spherical space which is either absolutely spherical or wave-front. It is shown that every tempered representation of G/H embeds into a relative discre…
The harmonic analysis of lattice counting on real spherical spaces
Bernhard Krötz, Eitan Sayag, Henrik Schlichtkrull
By the collective name of {\it lattice counting} we refer to a setup introduced in Duke-Rudnick-Sarnak that aim to establish a relationship between arithmetic and randomness in the…
Volume growth, temperedness and integrability of matrix coefficients on a real spherical space
Friedrich Knop, Bernhard Krötz, Eitan Sayag +1
We apply the local structure theorem and the polar decomposition to a real spherical space Z=G/H and control the volume growth on Z. We define the Harish-Chandra Schwartz space on…
Hausdorffness for Lie algebra homology of Schwartz spaces and applications to the comparison conjecture
Avraham Aizenbud, Dmitry Gourevitch, Bernhard Krötz +1
Let be a real algebraic group acting equivariantly with finitely many orbits on a real algebraic manifold and a real algebraic bundle on . Let $\mathfrak{h…
Simple compactifications and polar decomposition of homogeneous real spherical spaces
Friedrich Knop, Bernhard Krötz, Eitan Sayag +1
Let Z be an algebraic homogeneous space Z=G/H attached to real reductive Lie group G. We assume that Z is real spherical, i.e., minimal parabolic subgroups have open orbits on Z. F…
The local structure theorem for real spherical varieties
Friedrich Knop, Bernhard Krötz, Henrik Schlichtkrull
Let be an algebraic real reductive group and a real spherical -variety, that is, it admits an open orbit for a minimal parabolic subgroup . We prove a local structure…
Multiplicity bounds and the subrepresentation theorem for real spherical spaces
Bernhard Krötz, Henrik Schlichtkrull
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 s…
Finite orbit decomposition of real flag manifolds
Bernhard Krötz, Henrik Schlichtkrull
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 mani…
Decomposition Theorems for Triple Spaces
Thomas Danielsen, Bernhard Krötz, Henrik Schlichtkrull
A triple space is a homogeneous space where is a threefold product group and the diagonal subgroup of . This paper concerns the g…
Decay of matrix coefficients on reductive homogeneous spaces of spherical type
Bernhard Krötz, Eitan Sayag, Henrik Schlichtkrull
Let Z be a homogeneous space Z=G/H of a real reductive Lie group G with a reductive subgroup H. The investigation concerns the quantitative decay of matrix coefficients on unde…
Vanishing at infinity on homogeneous spaces of reductive type
Bernhard Krötz, Eitan Sayag, Henrik Schlichtkrull
Let G be a real reductive group and Z=G/H a unimodular homogeneous G-space. The space Z is said to satisfy VAI if all smooth vectors in the Banach representations L^{p}(Z) vanish a…
The complex crown for homogeneous harmonic spaces
Roberto Camporesi, Bernhard Krötz
A theory of holomorphic extension of eigenfunctions on homogeneous harmonic spaces is developed.
Invariant measures on homogeneous spaces, with applications to function spaces and lattice counting
Bernhard Krötz, Eitan Sayag, Henrik Schlichtkrull
Let G be a real reductive group and G/H a unimodular homogeneous G space with a closed connected subgroup H. We establish estimates for the invariant measure on G/H. Using these, w…