Stabilizers of Ergodic Actions of Lattices and Commensurators

By D. Creutz, J. Peterson. 2013

52 citations recorded by the source corpus.

We prove that any ergodic measure-preserving action of an irreducible lattice in a semisimple group, with finite center and each simple factor having rank at least two, either has finite orbits or has finite stabilizers. The same dichotomy holds for many commensurators of such lattices. The above are derived from more general results on groups with the Howe-Moore property and property $(T)$. We prove similar results for commensurators in such groups and for irreducible lattices (and commensurators) in products of at least two such groups, at least one of which is totally disconnected.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/17c44bca00b8cdc1b8dc978365a63d96aed67284

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In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Character rigidity for special linear groups (2013, background): “The cases m ≥ 3 are already covered by results of Stuck-Zimmer [35], Nevo-Zimmer [25], and Creutz and the first author [9].”
On the growth of $L^2$-invariants for sequences of lattices in Lie groups (2012, background): “3 were established recently in [42] and [80].”