Actions of Semisimple Lie Groups with Stationary Measure

Amos Nevo () and Robert J. Zimmer ()
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Amos Nevo: Technion, Department of Mathematics
Robert J. Zimmer: University of Chicago, Department of Mathematics

A chapter in Rigidity in Dynamics and Geometry, 2002, pp 321-343 from Springer

Abstract: Abstract We describe a new approach to the study of semisimple Lie group actions on compact manifolds (and more generally, Borel spaces), which uses the existence of a stationary measure as the basic tool. This approach was developed in [15]–[18], and we give here a coherent survey of the main results obtained. In addition, we give a complete account of the proofs of the main structure theorems for such actions (proved in [18]) in a simple, but nevertheless characteristic, model case.

Keywords: Parabolic Subgroup; Invariant Probability Measure; Poisson Boundary; Irreducible Lattice; Compact Metrizable Space (search for similar items in EconPapers)
Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-662-04743-9_17

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DOI: 10.1007/978-3-662-04743-9_17

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