Skip to main content
Log in

Sous-groupes discrets des groupes p-adiques de rang un et arbres de Bruhat-Tits

  • Published:
Israel Journal of Mathematics Aims and scope Submit manuscript

Abstract

Classically a colored tree is associated to any p-adic groups of rank one. For some of these, subgroups acting simply transitively on vertices of given color are constructed. In fewer case, the same can be done for edges.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • [B] H. Bass,Covering theory for graphs of groups, Journal of Pure and Applied Algebra89 (1993), 3–47.

    Article  MATH  MathSciNet  Google Scholar 

  • [B-K] H. Bass and R. Kulkarni,Uniform tree latices, Journal of the American Mathematical Society3 (1990), 843–902.

    Article  MATH  MathSciNet  Google Scholar 

  • [B-H] A. Borel and G. Harder,Existence of discrete cocompact subgroups of reductive groups over local fields, Journal für die reine und angewandte Mathematik298 (1978), 53–64.

    MATH  MathSciNet  Google Scholar 

  • [B-T 1 & 2] F. Bruhat et J. Tits,Schémas en groupes et immeubles des groupes classiques sur un corps local, 1re partie: le groupe linéaire général, Bulletin de la Société Mathématique de France112 (1984), 259–301; 2e partie: groupes unitaires Bulletin de la Société Mathématique de France115 (1987), 141–195.

    MATH  MathSciNet  Google Scholar 

  • [C-1] F. Choucroun,Analyse harmonique sur le groupe des automorphismes d’un arbre homogène et applications aux groupes libres, Comptes Rendus de l’Académie des Sciences, Paris296 (1983), 585–588.

    MATH  MathSciNet  Google Scholar 

  • [C-2] F. Choucroun,Groupes opérant simplement transitivement sur un arbre homogène et plongements dans PGL2(k), Comptes Rendus de l’Académie des Sciences, Paris298 (1984), 313–315.

    MATH  MathSciNet  Google Scholar 

  • [C-3] F. Choucroun,Analyse harmonique des groupes d’automorphismes d’arbre de Bruhat-Tits, Mémoires de la Societé Mathématique de France, supplément n058 au bulletin122 (1994), fasc. 3.

  • [F-P] A. Figa-Talamanca and M. A. Picardello,Restriction of spherical representation of PGL2 (ℚ P )to a discrete subgroup, Proceedings of the American Mathematical Society91 (1983), 405–408.

    Article  MathSciNet  Google Scholar 

  • [I] Y. Ihara,Dicrete subgroup of PGL2(k p), Proceedings of Symposia in Pure Mathematics9 (1966), 272–278.

    MathSciNet  Google Scholar 

  • [J] N. Jacobson,Basic Algebra II, Freeman and Company, San Francisco, 1989.

    MATH  Google Scholar 

  • [L-1] A. Lubotzky,Trees and discrete subgroups of Lie groups over local fields, Bulletin of the American Mathematical Society20 (1989), 27–30.

    MATH  MathSciNet  Google Scholar 

  • [L-2] A. Lubotzky,Lattices in rank one Lie groups over local fields, Geometric and Functional Analysis1 (1991), 406–431.

    Article  MathSciNet  Google Scholar 

  • [L-3] A. Lubotzky,Lattices of minimal covolume in SL2:a non-archimedian analogue of Siegel’s theorem μ ≥ π/21, Journal of the American Mathematical Society3 (1990), 961–975.

    Article  MATH  MathSciNet  Google Scholar 

  • [M-W] B. Mohar and W. Woess,A survey on spectra of infinite graphs, The Bulletin of the London Mathematical Society21 (1989), 209–234.

    Article  MATH  MathSciNet  Google Scholar 

  • [S] J. P. Serre,Arbres, amalgames, SL2, Astérisque46 (1977).

  • [T] J. Tits,Reductive groups over local fields, Proceedings of Symposia in Pure Mathematics33 (1979), 29–69.

    MathSciNet  Google Scholar 

  • [VdW] B. L. van der Waerden,Grouppen von linearen transformationen, Chelsea Publ. Co., New York, 1948.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Francis M. Choucroun.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Choucroun, F.M. Sous-groupes discrets des groupes p-adiques de rang un et arbres de Bruhat-Tits. Israel J. Math. 93, 195–219 (1996). https://doi.org/10.1007/BF02761103

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02761103

Navigation