Unique ergodicity on compact homogeneous spaces

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Extending results of a number of authors, we prove that if U is the unipotent radical of an ℝ-split solvable epimorphic subgroup of a real algebraic group G which is generated by unipotents, then the action of U on G/F is uniquely ergodic for every cocompact lattice F in G. 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.

Original languageEnglish
Pages (from-to)585-592
Number of pages8
JournalProceedings of the American Mathematical Society
Issue number2
StatePublished - 2001
Externally publishedYes


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