TY - JOUR

T1 - Unique ergodicity on compact homogeneous spaces

AU - Weiss, Barak

PY - 2001

Y1 - 2001

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=33646849288&partnerID=8YFLogxK

U2 - 10.1090/s0002-9939-00-05791-9

DO - 10.1090/s0002-9939-00-05791-9

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AN - SCOPUS:33646849288

VL - 129

SP - 585

EP - 592

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 2

ER -