Journal of Modern Dynamics (JMD)

Measures invariant under horospherical subgroups in positive characteristic

Pages: 237 - 254, Issue 2, April 2011      doi:10.3934/jmd.2011.5.237

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Amir Mohammadi - Department of Mathematics, University of Chicago, 5734 S. University Avenue, Chicago, IL 60637, United States (email)

Abstract: We prove measure rigidity for the action of maximal horospherical subgroups on homogeneous spaces over a field of positive characteristic. In the case when the lattice is uniform we prove the action of any horospherical subgroup is uniquely ergodic.

Keywords:  Invariant measures, measure rigidity, local fields, positive characteristic.
Mathematics Subject Classification:  Primary: 37D40, 37A17; Secondary: 22E40.

Received: July 2010;      Revised: February 2011;      Available Online: July 2011.