Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-27T04:49:11.549Z Has data issue: false hasContentIssue false
  • English
  • Français

Epimorphic subgroups and invariant measures

Published online by Cambridge University Press:  14 October 2010

Shahar Mozes
Shahar Mozes
Affiliation:
Department of Mathematics, Hebrew University, Jerusalem 91904 Israel
Get access Rights & Permissions [Opens in a new window]

Abstract

It is shown that a probability measure on a homogeneous space Γ\G which is invariant under a subgroup H < G which is epimorphic in a subgroup L < G is invariant under L. When L = G we obtain a subgroup H such that for any lattice Γ < G its action on Γ\G is uniquely ergodic.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 15 , Issue 6 , December 1995 , pp. 1207 - 1210
Copyright
Copyright © Cambridge University Press 1995

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[B-Bl]Bien, F. and Borel, A.. Sous-groupes épimorphiques de groupes linéaires algébriques I. C.R. Acad. Sci. Paris 315 (1992).Google Scholar
[B-B2]Bien, F. and Borel, A.. Sous-groupes épimorphiques de groupes linéaires algébriques II. C.R. Acad. Sci. Paris 315 (1992).Google Scholar
[M]Margulis, G. A.. Dynamical and ergodic properties of subgroup actions on homogeneous spaces with application to number theory. Proc. ICM. Kyoto, Japan, 1990. pp. 193–215.Google Scholar
[Rl]Ratner, M.. Strict measure rigidity for unipotent subgroups of solvable groups. Invent. Math. 101 (1990), 449–482.CrossRefGoogle Scholar
[R2]Ratner, M.. On measure rigidity of unipotent subgroups of semisimple groups. Acta. Math. 165 (1990), 229–309.CrossRefGoogle Scholar
[R3]Ratner, M.. On Raghunathan's measure conjecture. Ann. Math. 134 (1991), 545–607.CrossRefGoogle Scholar
[R4]Ratner, M.. Distribution rigidity for unipotent actions on homogeneous spaces. Bull. Amer. Math. Soc. 24 (1991), 321–325.CrossRefGoogle Scholar
[S]Shah, N.. Uniformly distributed orbits of certain flows on homogeneous spaces. Math. Ann. 289 (1991), 315–334.CrossRefGoogle Scholar