Letters in Mathematical Physics

, Volume 21, Issue 1, pp 77–84 | Cite as

Representation theoretical meaning of the initial value problem for the Toda lattice hierarchy: I

  • Takashi Takebe
Article

Abstract

The Toda lattice hierarchy is shown to have the Bruhat decomposition of the A group as its parameter space instead of the Grassmann manifold for the KP hierarchy. Takasaki's work on the initial value problem for the Toda lattice hierarchy is reinterpreted from this point of view.

AMS subject classifications (1980)

17B67 81E40 82A68 

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References

  1. 1.
    DateE., JimboM., and MiwaT., Transformation groups for soliton equations, Proc. RIMS Symp. Nonlinear Integrable Systems — Classical Theory and Quantum Theory (Kyoto 1981), World Scientific, Singapore, 1983, pp. 39–119.Google Scholar
  2. 2.
    JimboM. and MiwaT., Solitons and infinite-dimensional Lie algebras, Publ. RIMS Kyoto Univ. 19, 943–1001 (1983).Google Scholar
  3. 3.
    Kac, V. G., Infinite Dimensional Lie Algebras, 2nd edn., Cambridge Univ. Press, 1985.Google Scholar
  4. 4.
    KawamotoN., NamikawaY., TsuchiyaA. and YamadaY., Geometric realization of conformal field theory, Comm. Math. Phys. 116, 247–308 (1988).Google Scholar
  5. 5.
    Mimachi, K., Noumi, M., and Yamada, H., Finite-dimensional representations of the quantum group GLq(n+1; C) and the zonal spherical functions on Uq(n)/Uq(n+1). In preparation.Google Scholar
  6. 6.
    TakasakiK., Initial value problem for the Toda lattice hierarchy, Adv. Stud. Pure Math. 4, Group Representation and Systems of Differential Equations, Kinokuniya, Tokyo, 1984, pp. 139–163.Google Scholar
  7. 7.
    Takebe, T., Toda lattice hierarchy and conservation laws, Comm. Math. Phys. 129, 281–318.Google Scholar
  8. 8.
    UenoK. and TakasakiK., Toda lattice hierarchy, Adv. Stud. Pure Math. 4, Group Representation and Systems of Differential Equations, Kinokuniya, Tokyo, 1984, pp. 1–95.Google Scholar

Copyright information

© Kluwer Academic Publishers 1991

Authors and Affiliations

  • Takashi Takebe
    • 1
  1. 1.Department of Mathematics, Faculty of ScienceUniversity of TokyoTokyoJapan

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