Titlebook: Ergodic Theory and Semisimple Groups; Robert J. Zimmer Book 1984 Springer Science+Business Media New York 1984 Arithmetic.Identity.Lattice

走調(diào)

calorie

Inquiry, Engagement, and EducationIn this chapter we indicate how to extend some of the results of the preceding chapters to lattices and actions of groups which are (finite) products of semisimple groups over possibly varying local fields.

護(hù)航艦

Suggestions

Algebraic Groups and Measure Theory,In this section, we shall review without proof some basic notions concerning algebraic groups. For proofs and further details, we refer to the reader to the standard works on the subject, e.g. [Borel 1], [Humphreys 1], [Chevalley 1], [Borel-Tits 1], [Springer 1], [Steinberg 1].

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咒語

,Margulis’ Arithmeticity Theorems,We recall from the introduction the following construction of lattices.

雪崩

,Kazhdan’s Property (T),Let . be a locally compact (second countable) group and π:G → U(?) a unitary representation of . on the (separable) Hilbert space ?.Of course,? may or may not contain non-trivial vectors invariant under .(.). We wish to define a notion of . almost containing invariant vectors.

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