TY - JOUR

T1 - On measures invariant under tori on quotients of semisimple groups

AU - Einsiedler, Manfred

AU - Lindenstrauss, Elon

N1 - Publisher Copyright:
© 2015 Department of Mathematics, Princeton University.

PY - 2015

Y1 - 2015

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84923070507&partnerID=8YFLogxK

U2 - 10.4007/annals.2015.181.3.3

DO - 10.4007/annals.2015.181.3.3

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AN - SCOPUS:84923070507

SN - 0003-486X

VL - 181

SP - 993

EP - 1031

JO - Annals of Mathematics

JF - Annals of Mathematics

IS - 3

ER -