On measures invariant under tori on quotients of semisimple groups

• 成果类型: Article
• 署名作者: Einsiedler, Manfred; Lindenstrauss, Elon
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2015.181.3.3
• 发表日期: 2015
• 页码: 993-1031
• 关键词: diagonalizable actions; measure rigidity; FLOWS; joinings; Orbits

摘要

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.