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Systems of Toda type, inverse spectral problems, and representation theory. (English) Zbl 0474.58009


MSC:

37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
70H05 Hamilton’s equations
53D50 Geometric quantization
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References:

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[3] Adler, M.: On a Trace Functional for Formal Pseudo-Differential Operators and the Symplectic Structure of the Korteweg-de Vries Type Equations. Invent. Math.50, 219-248 (1979) · Zbl 0393.35058
[4] Adler, M.: Some Algebraic Relations Common to a Set of Integrable Partial and Ordinary Differential Equations. MRC Technical Summary Report #1801, University of Wisconsin-Madison 1977
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[15] Kirillov, A., Unitary Representations of Nilpotent Lie Groups. Russ. Math. Surveys17 (4) 57-101 (1962) · Zbl 0106.25001
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[18] Warner, G.: Harmonic Analysis on Semi-Simple Lie Groups I. New York: Springer-Verlag 1972 · Zbl 0265.22020
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[22] v. Moerbeke, P.: The Spectrum of Jacobi Matrices. Invent. Math.37, 45-81 (1976) · Zbl 0361.15010
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