Journal
ANNALS OF MATHEMATICS
Volume 181, Issue 3, Pages 993-1031Publisher
Princeton Univ, Dept Mathematics
DOI: 10.4007/annals.2015.181.3.3
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Funding
- SNF [200021-127145]
- ERC [267259]
- ISF [983/09]
- NSF [DMS-0800345]
- European Research Council (ERC) [267259] Funding Source: European Research Council (ERC)
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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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