×

Reduction of Hamiltonian systems, affine Lie algebras and Lax equations. (English) Zbl 0403.58004


MSC:

37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
22E65 Infinite-dimensional Lie groups and their Lie algebras: general properties
PDFBibTeX XMLCite
Full Text: DOI EuDML

References:

[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) · Zbl 0393.35058
[2] Arnol’d, V.I.: Mathematical methods of classical mechanics. Moscow: ?Nauka?, 1974 (Russian)
[3] Duflo, M.: Operateurs différentiels bi-invariants sur un groupe de Lie. Ann. Sci. École Norm. Sup., 4e série10, 1323-1367 (1977)
[4] Gohberg, I.Z., Feldman, I.A.: Convolution equations and projectional methods of their solution. Moscow: ?Nauka?, 1971 (Russian)
[5] Kac, V.G.: Simple irreducible graded Lie algebras of finite growth. Math. USSR, Izv.A2, 1271-1311 (1978) · Zbl 0222.17007
[6] Kac, V.G.: Automorphisms of finite order of semisimple Lie algebras. Functional analysis and its applications,3, 94-96 (1969)
[7] Kazhdan, D., Kostant, B., Sternberg, S.: Hamiltonian group actions and dynamical systems of Calogero type. Comm. Pure Appl. Math.,31, 481-508 (1978) · Zbl 0368.58008
[8] Kirillov, A.A.: Elements de la théorie des représentations. Moscou: Editions Mir, 1974
[9] Kostant, B.: On Whittaker vectors and representation theory. Inventiones math.,48, 101-184 (1978) · Zbl 0405.22013
[10] Kostant, B.: Quantization and unitary representations I. In: Lecture Notes in Mathematics, v. 170, pp. 87-208. Berlin-Heidelberg-New York: Springer 1970 · Zbl 0223.53028
[11] Kritchever, I.M.: Algebraic curves and nonlinear difference equations. Uspekhi Mat. Nauk33, 215-216 (1978) (Russian)
[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)
[13] Mischenko, A.S., Fomenko, A.T.: Euler equations on finite-dimensional Lie groups. Izwestija AN SSSR (ser. matem.)42, 396-415 (1978) (Russian)
[14] Moody, R.V.: A new class of Lie algebras. J. Algebra10, 211-230 (1968) · Zbl 0191.03005
[15] Moser, J.: Various aspects of integrable Hamiltonian systems. preprint · Zbl 0468.58011
[16] Olshanetsky, M.A., Perelomov, A.M.: Explicit solutions of the classical generalized Toda models. Preprint ITEP-157, 1978 · Zbl 0419.58008
[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)
[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)
[19] Zakharov, V.E., Mikhailov, A.V.: Two-dimensional relativistic models of classical field theory. ZETP,74, 1953-1973 (1978) (Russian)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.