Groups, Geometry, and Dynamics

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Volume 11, Issue 3, 2017, pp. 1003–1039
DOI: 10.4171/GGD/420

Published online: 2017-08-22

Equicontinuous actions of semisimple groups

Uri Bader[1] and Tsachik Gelander[2]

(1) Technion - Israel Institute of Technology, Haifa, Israel
(2) The Weizmann Institute of Science, Rehovot, Israel

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.

Keywords: Howe–Moore Theorem, Mautner’s phenomenon, uniform structures, metric ergodicity, WAP-representations

Bader Uri, Gelander Tsachik: Equicontinuous actions of semisimple groups. Groups Geom. Dyn. 11 (2017), 1003-1039. doi: 10.4171/GGD/420