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Inventiones mathematicae

, Volume 54, Issue 1, pp 81–100 | Cite as

Reduction of Hamiltonian systems, affine Lie algebras and Lax equations

  • A. G. Reyman
  • M. A. Semenov-Tian-Shansky
Article

Keywords

Hamiltonian System 
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References

  1. 1.
    Adler, M.: On a trace functional for formal pseudodifferential operators and the symplectic structure for Korteweg-de-Vries type equations. Inventiones math.50, 219–248 (1979)Google Scholar
  2. 2.
    Arnol'd, V.I.: Mathematical methods of classical mechanics. Moscow: “Nauka”, 1974 (Russian)Google Scholar
  3. 3.
    Duflo, M.: Operateurs différentiels bi-invariants sur un groupe de Lie. Ann. Sci. École Norm. Sup., 4e série10, 1323–1367 (1977)Google Scholar
  4. 4.
    Gohberg, I.Z., Feldman, I.A.: Convolution equations and projectional methods of their solution. Moscow: “Nauka”, 1971 (Russian)Google Scholar
  5. 5.
    Kac, V.G.: Simple irreducible graded Lie algebras of finite growth. Math. USSR, Izv.A2, 1271–1311 (1978)Google Scholar
  6. 6.
    Kac, V.G.: Automorphisms of finite order of semisimple Lie algebras. Functional analysis and its applications,3, 94–96 (1969)Google Scholar
  7. 7.
    Kazhdan, D., Kostant, B., Sternberg, S.: Hamiltonian group actions and dynamical systems of Calogero type. Comm. Pure Appl. Math.,31, 481–508 (1978)Google Scholar
  8. 8.
    Kirillov, A.A.: Elements de la théorie des représentations. Moscou: Editions Mir, 1974Google Scholar
  9. 9.
    Kostant, B.: On Whittaker vectors and representation theory. Inventiones math.,48, 101–184 (1978)Google Scholar
  10. 10.
    Kostant, B.: Quantization and unitary representations I. In: Lecture Notes in Mathematics, v. 170, pp. 87–208. Berlin-Heidelberg-New York: Springer 1970Google Scholar
  11. 11.
    Kritchever, I.M.: Algebraic curves and nonlinear difference equations. Uspekhi Mat. Nauk33, 215–216 (1978) (Russian)Google Scholar
  12. 12.
    Manakov, S.V.: A notice concerning the integration of Euler's equation for then-dimensional rigid body. Funct. Anal. and its Applications,10, 93–95 (1968)Google Scholar
  13. 13.
    Mischenko, A.S., Fomenko, A.T.: Euler equations on finite-dimensional Lie groups. Izwestija AN SSSR (ser. matem.)42, 396–415 (1978) (Russian)Google Scholar
  14. 14.
    Moody, R.V.: A new class of Lie algebras. J. Algebra10, 211–230 (1968)CrossRefGoogle Scholar
  15. 15.
    Moser, J.: Various aspects of integrable Hamiltonian systems. preprintGoogle Scholar
  16. 16.
    Olshanetsky, M.A., Perelomov, A.M.: Explicit solutions of the classical generalized Toda models. Preprint ITEP-157, 1978Google Scholar
  17. 17.
    Reyman, A.G., Semenov-Tian-Shansky, M.A., Frenckel, I.B.: Affine Lie algebras and completely integrable Hamiltonian systems, Sov. Math. Doklady ANSSSR247, 802–805 (1979) (Russian) =Sov. Math. (Doklady), in press (1979)Google Scholar
  18. 18.
    Shubov, V.I.: On decomposition of the quasiregular representations of Lie groups via the orbits' method. Zapisky Nauchnych Seminarov LOMI37, 77–99 (1973) (Russian)Google Scholar
  19. 19.
    Zakharov, V.E., Mikhailov, A.V.: Two-dimensional relativistic models of classical field theory. ZETP,74, 1953–1973 (1978) (Russian)Google Scholar

Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • A. G. Reyman
    • 1
  • M. A. Semenov-Tian-Shansky
    • 1
  1. 1.Leningrad Branch of the V.A. Steklov Mathematical InstituteLeningradUSSR

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