Unique ergodicity on compact homogeneous spaces

Author:
Barak Weiss

Journal:
Proc. Amer. Math. Soc. **129** (2001), 585-592

MSC (1991):
Primary 22F30

DOI:
https://doi.org/10.1090/S0002-9939-00-05791-9

Published electronically:
August 28, 2000

MathSciNet review:
1800240

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Abstract | References | Similar Articles | Additional Information

Extending results of a number of authors, we prove that if is the unipotent radical of an -split solvable epimorphic subgroup of a real algebraic group which is generated by unipotents, then the action of on is uniquely ergodic for every cocompact lattice in . This gives examples of uniquely ergodic and minimal two-dimensional flows on homogeneous spaces of arbitrarily high dimension. Our main tools are the Ratner classification of ergodic invariant measures for the action of a unipotent subgroup on a homogeneous space, and a simple lemma (the `Cone Lemma') about representations of epimorphic subgroups.

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Additional Information

**Barak Weiss**

Affiliation:
Department of Mathematics, State University of New York at Stony Brook, Stony Brook, New York 11794

Email:
barak@math.sunysb.edu

DOI:
https://doi.org/10.1090/S0002-9939-00-05791-9

Received by editor(s):
April 22, 1999

Published electronically:
August 28, 2000

Communicated by:
Michael Handel

Article copyright:
© Copyright 2000
American Mathematical Society