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Minimality and unique ergodicity for subgroup actions

Shahar MozesBarak Weiss — 1998

Annales de l'institut Fourier

Let G be an -algebraic semisimple group, H an algebraic -subgroup, and Γ a lattice in G . Partially answering a question posed by Hillel Furstenberg in 1972, we prove that if the action of H on G / Γ is minimal, then it is uniquely ergodic. Our proof uses in an essential way Marina Ratner’s classification of probability measures on G / Γ invariant under unipotent elements, and the study of “tubes” in G / Γ .

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