Duke Mathematical Journal

Raghunathan’s conjectures for Cartesian products of real and $\mathfrak{p}$-adic Lie groups

Marina Ratner

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Duke Math. J. Volume 77, Number 2 (1995), 275-382.

First available in Project Euclid: 20 February 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 22E40: Discrete subgroups of Lie groups [See also 20Hxx, 32Nxx]
Secondary: 22E50: Representations of Lie and linear algebraic groups over local fields [See also 20G05]


Ratner, Marina. Raghunathan’s conjectures for Cartesian products of real and 𝔭 -adic Lie groups. Duke Math. J. 77 (1995), no. 2, 275--382. doi:10.1215/S0012-7094-95-07710-2. http://projecteuclid.org/euclid.dmj/1077286345.

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  • [B] A. Borel, Linear Algebraic Groups, 2nd enl. ed., Graduate Texts in Math., vol. 126, Springer-Verlag, New York, 1991.
  • [BP] A. Borel and G. Prasad, Values of isotropic quadratic forms at $S$-integral points, Compositio Math. 83 (1992), no. 3, 347–372.
  • [D1] S. G. Dani, A simple proof of Borel's density theorem, Math. Z. 174 (1980), no. 1, 81–94.
  • [D2] S. G. Dani, On orbits of unipotent flows on homogeneous spaces. II, Ergodic Theory Dynam. Systems 6 (1986), no. 2, 167–182.
  • [DM] S. G. Dani and G. A. Margulis, Limit distributions of orbits of unipotent flows and values of quadratic forms, I. M. Gelfand Seminar, Adv. Soviet Math, vol. 16, Amer. Math. Soc., Providence, 1993, pp. 91–137.
  • [DSMS] J. D. Dixon, M. P. F. du Sautoy, A. Mann, and D. Segal, Analytic Pro-$p$ Groups, London Math. Soc. Lecture Note Ser., vol. 157, Cambridge Univ. Press, Cambridge, 1991.
  • [J] N. Jacobson, Lie Algebras, Dover, New York, 1979.
  • [M1] G. A. Margulis, Discrete Subgroups of Semisimple Lie Groups, Ergeb. Math. Grenzgeb (3), vol. 17, Springer-Verlag, Berlin, 1991.
  • [M2] G. A. Margulis, Discrete subgroups and ergodic theory, Number Theory, Trace Formulas and Discrete Groups (Oslo, 1987), Academic Press, Boston, 1989, pp. 377–398.
  • [MT] G. A. Margulis and G. M. Tomanov, Invariant measures for actions of unipotent groups over local fields on homogeneous spaces, Invent. Math. 116 (1994), no. 1-3, 347–392.
  • [P] G. Prasad, Ratner's theorem in $S$-arithmetic setting, Workshop on Lie Groups, Ergodic Theory and Geometry, Math. Sci. Res. Inst. Publ., Springer-Verlag, New York, 1992, p. 53.
  • [Ra] M. S. Raghunathan, Discrete Subgroups of Lie Groups, Ergeb. Math. Grenzgeb., vol. 68, Springer-Verlag, New York, 1972.
  • [R1] M. Ratner, Strict measure rigidity for unipotent subgroups of solvable groups, Invent. Math. 101 (1990), no. 2, 449–482.
  • [R2] M. Ratner, On measure rigidity of unipotent subgroups of semisimple groups, Acta Math. 165 (1990), no. 3-4, 229–309.
  • [R3] M. Ratner, On Raghunathan's measure conjecture, Ann. of Math. (2) 134 (1991), no. 3, 545–607.
  • [R4] M. Ratner, Raghunathan's topological conjecture and distributions of unipotent flows, Duke Math. J. 63 (1991), no. 1, 235–280.
  • [R5] M. Ratner, Invariant measures and orbit closures for unipotent actions on homogeneous spaces, Geom. Funct. Anal. 4 (1994), no. 2, 236–257.
  • [R6] M. Ratner, Raghunathan's conjectures for $p$-adic Lie groups, Internat. Math. Res. Notices (1993), no. 5, 141–146.
  • [S] J.-P. Serre, Lie Algebras and Lie Groups, Lectures given at Harvard University, vol. 1964, Benjamin, New York-Amsterdam, 1965.
  • [T] T. Tamagawa, On discrete subgroups of $p$-adic algebraic groups, Arithmetical Algebraic Geometry (Proc. Conf. Purdue Univ., 1963), Harper and Row, New York, 1965, pp. 11–17.
  • [Te] A. Tempelman, Ergodic Theorems for Group Actions, Math. Appl., vol. 78, Kluwer, Dordrecht, 1992.
  • [V] B. L. Van der Waerden, Modern Algebra, Frederick Ungar Publ. Co., New York, 1953.
  • [W] D. Witte, Zero-entropy affine maps on homogeneous spaces, Amer. J. Math. 109 (1987), no. 5, 927–961.