Unique ergodicity on compact homogeneous spaces

Research output: Contribution to journalArticlepeer-review

Abstract

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
Volume129
Issue number2
DOIs
StatePublished - 2001
Externally publishedYes

Fingerprint

Dive into the research topics of 'Unique ergodicity on compact homogeneous spaces'. Together they form a unique fingerprint.

Cite this