On measures invariant under tori on quotients of semisimple groups

Manfred Einsiedler; Elon Lindenstrauss

doi:https://doi.org/10.4007/annals.2015.181.3.3

Abstract

We classify invariant and ergodic probability measures on arithmetic homogeneous quotients of semisimple $S$-algebraic groups invariant under a maximal split torus in at least one simple local factor and show that the algebraic support of such a measure splits into the product of four homogeneous spaces: a torus, a homogeneous space on which the measure is (up to finite index) the Haar measure, a product of homogeneous spaces on each of which the action degenerates to a rank one action, and a homogeneous space in which every element of the action acts with zero entropy.

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On measures invariant under tori on quotients of semisimple groups

Abstract

Authors