Geodesic
On measures invariant under tori on quotients of semisimple groups
Manfred Einsiedler1 ; Elon Lindenstrauss2
1 ETH Zürich, Zürich, Switzerland
2 Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel
Annals of mathematics, Tome 181 (2015) no. 3, pp. 993-1031.

Voir la notice de l'article provenant de la source Annals of Mathematics website

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.
DOI : 10.4007/annals.2015.181.3.3

Manfred Einsiedler 1 ; Elon Lindenstrauss 2

1 ETH Zürich, Zürich, Switzerland
2 Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel 
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Manfred Einsiedler; Elon Lindenstrauss. On measures invariant under tori on quotients of semisimple groups. Annals of mathematics, Tome 181 (2015) no. 3, pp. 993-1031. doi : 10.4007/annals.2015.181.3.3. http://geodesic.mathdoc.fr/articles/10.4007/annals.2015.181.3.3/

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