Abstract
We show that many natural classes of actions of discrete subgroups of semisimple Lie groups have discrete spectrum, i.e., are measurably conjugate to isometric actions.
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References
G. W. Mackey,Ergodic transformation groups with a pure point spectrum, Ill. J. Math.6 (1962), 327–335.
G. A. Margulis,Discrete Subgroups of Semisimple Lie Groups, Springer, Berlin (to appear).
J. Moser,On the volume elements on a manifold, Trans. Amer. Math. Soc.120 (1965), 286–294.
R. J. Zimmer,Ergodic actions with generalized discrete spectrum, Ill. J. Math.20 (1976), 555–588.
R. J. Zimmer,Volume preserving actions of lattices in semisimple groups on compact manifolds, Publ. Math. I.H.E.S.59 (1984), 5–33.
R. J. Zimmer,Kazhdan groups acting on compact manifolds, Invent. Math.75 (1984), 425–436.
R. J. Zimmer,Lattices in semismple groups and invariant geometric structures on compact manifolds, inDiscrete Groups in Geometry and Analysis (R. Howe, ed.), Birkhauser, Boston, 1987, pp. 152–210.
R. J. Zimmer,Ergodic Theory and Semisimple Groups, Birkhauser, Boston, 1984.
R. J. Zimmer,Actions of semisimple groups and discrete groups, Proc. ICM, Berkeley, 1986, pp.1247–1258.
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Research partially supported by NSF Grant.
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Zimmer, R.J. Spectrum, entropy, and geometric structures for smooth actions of kazhdan groups. Israel J. Math. 75, 65–80 (1991). https://doi.org/10.1007/BF02787182
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DOI: https://doi.org/10.1007/BF02787182