Bulletin (New Series) of the American Mathematical Society

Trees and discrete subgroups of Lie groups over local fields

Alexander Lubotzky

Full-text: Open access

Article information

Source
Bull. Amer. Math. Soc. (N.S.), Volume 20, Number 1 (1989), 27-30.

Dates
First available in Project Euclid: 4 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.bams/1183554900

Mathematical Reviews number (MathSciNet)
MR945301

Zentralblatt MATH identifier
0676.22007

Subjects
Primary: 22E40: Discrete subgroups of Lie groups [See also 20Hxx, 32Nxx]
Secondary: 20G25: Linear algebraic groups over local fields and their integers

Citation

Lubotzky, Alexander. Trees and discrete subgroups of Lie groups over local fields. Bull. Amer. Math. Soc. (N.S.) 20 (1989), no. 1, 27--30. https://projecteuclid.org/euclid.bams/1183554900


Export citation

References

  • [B] H. Behr, Finite presentability of arithmetic groups over global function fields, Proc. Edinburgh Math. Soc. 30 (1987), 23-39.
  • [BL] H. Bass and A. Lubotzky (in preparation).
  • [BT] F. Bruhat and J. Tits, Groupes algébriques simples sur un corps locals, Proc. Conf. on Local Fields (T. A. Springer, ed.) (Driebergen) Springer-Verlag, New York, 1967, pp. 23-36.
  • [DM] P. Deligne and G. D. Mostow, Monodromy of hypergeometric functions and non lattice integral monodromy groups, Inst. Hautes Études Sci. Publ. Math. 63 (1986), 5-90.
  • [E] P. Eberlein, Lattices in spaces of non positive curvature, Ann. of Math. (2) 111 (1980), 435-476.
  • [GP] L. Gerritzen and M. van der Put, Schottky groups and Mumford curves, Lecture Notes in Math., vol. 817, Springer-Verlag, New York, 1980.
  • [GPS] M. Gromov and I. Piatetski-Shapiro, Non-arithmetic groups in Lobachevsky spaces, Inst. Hautes Études Sci. Publ. Math. 66 (1988), 93-103.
  • [GR] H. Garland and M. S. Raghunathan, Fundamental domains for lattices in (R)-rank1 semisimple Lie groups, Ann. of Math. (2) 92 (1970), 279-326.
  • [I] Y. Ihara, On discrete subgroups of the two by two projective linear group over p-adic fields, J. Math. Soc. Japan 18 (1966), 219-235.
  • [Ka] D. A. Kazdhan, Some applications of the Weil representation, J. Analyse Math. 32 (1977), 235-248.
  • [L1] A. Lubotzky, Group presentation, p-adic analytic groups and lattices in SL2(C), Ann. of Math. (2) 118 (1983), 115-130.
  • [L2] A. Lubotzky, Lattices in rank one semisimple Lie groups over local fields (in preparation).
  • [Ma] G. A. Margulis, Arithmeticity of irreducible lattices in the semi-simple groups of rank greater than 1, Invent Math. 76 (1984), 93-120.
  • [Mi] J. J. Millson, On the first Betti number of constant negative curved manifold, Ann. of Math. (2) 104 (1976), 235-247.
  • [M1] G. D. Mostow, Strong rigidity of locally symmetric spaces, Ann. of Math. Stud., no. 78, Princeton Univ. Press, Princeton, N.J., 1973.
  • [M2] G. D. Mostow, On a remarkable class of polyhedra in complex hyperbolic space, Pacific J. Math. 86(1980), 171-276.
  • [R1] M. S. Raghunathan, On the congruence subgroup problem, Inst. Hautes Études Sci. Publ. Math. 46 (1976), 107-161.
  • [R2] M. S. Raghunathan, On the congruence subgroups problem. II, Invent. Math. 85 (1986), 73-117.
  • [S1] J.-P. Serre, Le problème des groupes de congruence pour SL2, Ann. of Math. (2) 92 (1970), 489-527.
  • [S2] J.-P. Serre, Trees, Springer-Verlag, New York, 1980.
  • [Z] R. Zimmer, Ergodic theory and semi-simple groups, Birkhäuser, Boston, 1984.