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Proceedings of the London Mathematical Society Advance Access published online on July 29, 2009
Proceedings of the London Mathematical Society, doi:10.1112/plms/pdp029
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© 2009 London Mathematical Society

Rigidity of measures invariant under semisimple groups in positive characteristic

Manfred Einsiedler

Mathematics Department
The Ohio State University
231 W. 18th Avenue
Columbus
OH 43210
USA
manfred@math.ohio-state.edu

Anish Ghosh

School of Mathematics
University of East Anglia
Norwich
NR4 7TJ
United Kingdom

Received 11 November 2008. Revision received 28 April 2009.

M. Ratner has conjectured a positive characteristic version of her seminal results classifying orbit closures and invariant measures of unipotent flows on homogeneous spaces. In this paper, we provide a partial answer by establishing a positive characteristic version of her classification result for measures invariant under semisimple groups.

2000 Mathematics Subject Classification 37D40, 37A17, 22E40.

M.E. was supported by DMS grant 0622397 and A.G. gratefully acknowledges the support of NSF and EPSRC.


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