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References
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)
Arnol'd, V.I.: Mathematical methods of classical mechanics. Moscow: “Nauka”, 1974 (Russian)
Duflo, M.: Operateurs différentiels bi-invariants sur un groupe de Lie. Ann. Sci. École Norm. Sup., 4e série10, 1323–1367 (1977)
Gohberg, I.Z., Feldman, I.A.: Convolution equations and projectional methods of their solution. Moscow: “Nauka”, 1971 (Russian)
Kac, V.G.: Simple irreducible graded Lie algebras of finite growth. Math. USSR, Izv.A2, 1271–1311 (1978)
Kac, V.G.: Automorphisms of finite order of semisimple Lie algebras. Functional analysis and its applications,3, 94–96 (1969)
Kazhdan, D., Kostant, B., Sternberg, S.: Hamiltonian group actions and dynamical systems of Calogero type. Comm. Pure Appl. Math.,31, 481–508 (1978)
Kirillov, A.A.: Elements de la théorie des représentations. Moscou: Editions Mir, 1974
Kostant, B.: On Whittaker vectors and representation theory. Inventiones math.,48, 101–184 (1978)
Kostant, B.: Quantization and unitary representations I. In: Lecture Notes in Mathematics, v. 170, pp. 87–208. Berlin-Heidelberg-New York: Springer 1970
Kritchever, I.M.: Algebraic curves and nonlinear difference equations. Uspekhi Mat. Nauk33, 215–216 (1978) (Russian)
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)
Mischenko, A.S., Fomenko, A.T.: Euler equations on finite-dimensional Lie groups. Izwestija AN SSSR (ser. matem.)42, 396–415 (1978) (Russian)
Moody, R.V.: A new class of Lie algebras. J. Algebra10, 211–230 (1968)
Moser, J.: Various aspects of integrable Hamiltonian systems. preprint
Olshanetsky, M.A., Perelomov, A.M.: Explicit solutions of the classical generalized Toda models. Preprint ITEP-157, 1978
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)
Shubov, V.I.: On decomposition of the quasiregular representations of Lie groups via the orbits' method. Zapisky Nauchnych Seminarov LOMI37, 77–99 (1973) (Russian)
Zakharov, V.E., Mikhailov, A.V.: Two-dimensional relativistic models of classical field theory. ZETP,74, 1953–1973 (1978) (Russian)
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Reyman, A.G., Semenov-Tian-Shansky, M.A. Reduction of Hamiltonian systems, affine Lie algebras and Lax equations. Invent Math 54, 81–100 (1979). https://doi.org/10.1007/BF01391179
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DOI: https://doi.org/10.1007/BF01391179