Equicontinuous actions of semisimple groups

Uri Bader; Tsachik Gelander

doi:10.4171/GGD/420

Equicontinuous actions of semisimple groups

Uri Bader, Tsachik Gelander

Mathematics

Research output: Contribution to journal › Article › peer-review

21 Scopus citations

Abstract

We study equicontinuous actions of semisimple groups and some generalizations. We prove that any such action is universally closed, and in particular proper. We derive various applications, both old and new, including closedness of continuous homomorphisms, nonexistence of weaker topologies, metric ergodicity of transitive actions and vanishing of matrix coefficients for reflexive (more generally: WAP) representations.

Original language	English (US)
Pages (from-to)	1003-1039
Number of pages	37
Journal	Groups, Geometry, and Dynamics
Volume	11
Issue number	3
DOIs	https://doi.org/10.4171/GGD/420
State	Published - 2017

Funding

1 The research was partly supported by the ERC and the ISF.

Keywords

Howe-Moore Theorem
Mautner's phenomenon
Metric ergodicity
Uniform structures
WAP-representations

ASJC Scopus subject areas

Geometry and Topology
Discrete Mathematics and Combinatorics

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10.4171/GGD/420

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keywords = "Howe-Moore Theorem, Mautner's phenomenon, Metric ergodicity, Uniform structures, WAP-representations",

author = "Uri Bader and Tsachik Gelander",

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AU - Gelander, Tsachik

N1 - Funding Information: 1 The research was partly supported by the ERC and the ISF. Publisher Copyright: © European Mathematical Society.

PY - 2017

Y1 - 2017

N2 - We study equicontinuous actions of semisimple groups and some generalizations. We prove that any such action is universally closed, and in particular proper. We derive various applications, both old and new, including closedness of continuous homomorphisms, nonexistence of weaker topologies, metric ergodicity of transitive actions and vanishing of matrix coefficients for reflexive (more generally: WAP) representations.

AB - We study equicontinuous actions of semisimple groups and some generalizations. We prove that any such action is universally closed, and in particular proper. We derive various applications, both old and new, including closedness of continuous homomorphisms, nonexistence of weaker topologies, metric ergodicity of transitive actions and vanishing of matrix coefficients for reflexive (more generally: WAP) representations.

KW - Howe-Moore Theorem

KW - Mautner's phenomenon

KW - Metric ergodicity

KW - Uniform structures

KW - WAP-representations

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ER -

Equicontinuous actions of semisimple groups

Abstract

Funding

Keywords

ASJC Scopus subject areas

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