On measures invariant under tori on quotients of semisimple groups

Manfred Einsiedler, Elon Lindenstrauss

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


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 homoge- neous 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.

Original languageAmerican English
Pages (from-to)993-1031
Number of pages39
JournalAnnals of Mathematics
Issue number3
StatePublished - 2015

Bibliographical note

Publisher Copyright:
© 2015 Department of Mathematics, Princeton University.


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