On Measures Invariant under Tori on Quotients of Semisimple Groups


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… (More)


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