215 citations · 807 across the 39 of their papers we have counts for
17 papers · 1 filter
Spherical subgroups in reductive algebraic groups
Friedrich Knop, Gerhard Roehrle
In a paper from 2015, we determined all spherical affine homogeneous varieties for simple algebraic groups in arbitrary characteristic. The present paper extends this classificatio…
Classification of toric projective varieties up to projective automorphisms
Friedrich Knop, Rainer Sinn
Toric subvarieties of projective space are classified up to projective automorphisms.
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…
Functoriality properties of the dual group
Friedrich Knop
Let be a connected reductive group. In a previous paper, arxiv:1702.08264, is was shown that the dual group attached to a -variety admits a natural homomorphi…
The dual group of a spherical variety
Friedrich Knop, Barbara Schalke
Let be a spherical variety for a connected reductive group . Work of Gaitsgory-Nadler strongly suggests that the Langlands dual group of has a subgroup whose We…
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…
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…
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…
Localization of spherical varieties
Friedrich Knop
We prove some fundamental structural results for spherical varieties in arbitrary characteristic. In particular, we study Luna's two types of localization and use it to analyze sph…
On the Kazhdan-Lusztig basis of a spherical Hecke algebra
Friedrich Knop
Lusztig proved that the Kazhdan-Lusztig basis of a spherical Hecke algebra can be essentially identified with the Weyl characters of the Langlands dual group. We generalize this re…
On Noether's and Weyl's bound in positive characteristic
Friedrich Knop
In this note we generalize several well known results concerning invariants of finite groups from characteristic zero to positive characteristic not dividing the group order. The f…
Combinatorics and invariant differential operators on multiplicity free spaces
Friedrich Knop
We study the generalization of shifted Jack polynomials to arbitrary multiplicity free spaces. In a previous paper (math.RT/0006004) we showed that these polynomials are eigenfunct…
Construction of commuting difference operators for multiplicity free spaces
Friedrich Knop
We study root systems equipped with a basis of dominant weights such that certain axioms hold. This formalism allows to define a linear basis P of the space of Weyl group invariant…
Semisymmetric polynomials and the invariant theory of matrix vector pairs
Friedrich Knop
In this paper we introduce and investigate a one-parameter family of polynomials. They are semisymmetric, i.e. symmetric in the variables with odd and even index separately. In fac…