Communications in Mathematical Physics

, Volume 159, Issue 3, pp 539–547 | Cite as

On geometrical interpretation of thep-adic Maslov index

  • E. I. Zelenov
Article

Abstract

A set of selfdual lattices Λ in a two-dimensionalp-adic symplectic space
is provided by an integer valued metricd. A realization of the metric space (Λ,d) as a graph Γ is suggested and this graph has been linked to the Bruhat-Tits tree. An action of symplectic group
on a set of cycles of length three of the graph Γ is considered and a geometrical interpretation of thep-adic Maslov index is given in terms of this action.

Keywords

Neural Network Statistical Physic Complex System Nonlinear Dynamics Quantum Computing 

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References

  1. [GP] Gerritzen, L., van der Put, M.: Schottky groups and Mumford curves. Lect. Notes in Math.817. Berlin, Heidelberg, New York: Springer 1980Google Scholar
  2. [L] Lang, S.: Algebra, Reading, MA: Addison-Wesley 1965Google Scholar
  3. [MH] Milnor, J., Husemoller, D.: Symmetric bilinear forms. Berlin, Heidelberg, New York: Springer 1973Google Scholar
  4. [M] Mumford, D.: An analytic construction of degenerating curves over complete local fields. Composito Math.24, 129 (1972)Google Scholar
  5. [S] Serre, J.-P.: Abres, amalgames,SL 2. Asterisque46 (1977)Google Scholar
  6. [VV] Vladimirov, V.S., Volovich, I.V.:p-Adic quantum mechanics. Commun. Math. Phys.123, 659–676 (1989)CrossRefGoogle Scholar
  7. [W] Weil, A.: Basic number theory. Berlin, Heidelberg, New York: Springer 1967Google Scholar
  8. [Z] Zelenov, E.I.:p-Adic Heisenberg group and the Maslov index. Commun. Math. Phys.155, 489–502 (1993)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • E. I. Zelenov
    • 1
  1. 1.Steklov Mathematical InstituteMoscowRussia

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