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Construction of canonical coordinates on polarized coadjoint orbits of Lie groups

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Construction of canonical coordinates on polarized coadjoint orbits of Lie groups is presented.

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References

  1. Adler, M.: On a trace functional, pseudo-differential operator and the symplectic structure of the KdV type equations. Invent. Math.50, 219–248 (1979)

    Google Scholar 

  2. Kostant, B.: The solutions to a generalized Toda lattice and representation theory. Adv. Math.34, 195–338 (1979)

    Google Scholar 

  3. Reyman, A.G., Semenov-Tian-Shansky, M.A.: Reduction of Hamiltonian systems, affine Lie algebras and Lax equations. Invent. Math.54, 81–100 (1979)

    Google Scholar 

  4. Symes, W.W.: Systems of Toda type, inverse spectral problems, and representation theory. Invent. Math.59, 13–51 (1980)

    Google Scholar 

  5. Symes, W.W.: Hamiltonian group actions and integrable systems. Physica D1, 339–374 (1980)

    Google Scholar 

  6. Novikov, S.P., Shmeltzer, I.: Periodic solutions to Kirchhoff equations for a free motion of a rigid body in fluid and Lusternik-Shnirelman-Morse extended theory (LSM). I. Funct. Anal. Appl.15, 54–66 (1981)

    Google Scholar 

  7. Kamalin, S.A., Perelomov, A.M.: Construction of canonical coordinates on coadjoint orbits of graded Lie groups. Preprint ITEP-86 (1983)

  8. Goodman, R., Wallach, N.R.: Classical and quantum mechanical systems of Toda lattice type. II. Solutions of the classical flows. Preprint of Rutgers University, 1983

  9. Vergne, M.: Construction de sous-algebres subordonnees a un element du dual d'une algebre de Lie resoluble. C.R. Acad. Sci.270, 173–175 (1970)

    Google Scholar 

  10. Kirillov, A.A.: Elements of the theory of representations. Berlin, Heidelberg, New York: Springer 1976

    Google Scholar 

  11. Diximier, J.: Algebres enveloppantes. Paris, Bruxelles, Montreal: Gauthier-Villars, 1974

    Google Scholar 

  12. Fuks, D.B., Fomenko, A.T., Gutenmacher, V.L.: Homotopic topology. Moscow: Moscow University 1969

    Google Scholar 

  13. Bourbaki, N.: Groupes et algebres de Lie. Chap. VII, VIII. (Elements de mathematique, Fasc. XXXVII). Paris: Hermann 1975

    Google Scholar 

  14. Bourbaki, N.: Groupes et algebres de Lie. Chap. IV-VI. (Elements de mathematique, Fasc. XXXIV). Paris: Hermann 1968

    Google Scholar 

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Authors and Affiliations

  1. Institute of Theoretical and Experimental Physics, SU-117259, Moscow, USSR

    S. A. Kamalin & A. M. Perelomov

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  1. S. A. Kamalin
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  2. A. M. Perelomov
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Communicated by Ya. G. Sinai

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Kamalin, S.A., Perelomov, A.M. Construction of canonical coordinates on polarized coadjoint orbits of Lie groups. Commun.Math. Phys. 97, 553–568 (1985). https://doi.org/10.1007/BF01221217

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  • DOI: https://doi.org/10.1007/BF01221217

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