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Linearization of Hamiltonian systems, Jacobi varieties and representation theory. (English) Zbl 0455.58010
In the note under review the authors show that all systems discussed in their previous note [Adv. Math. 38, 267–317 (1980; Zbl 0455.58017)] can be linearized according to a general scheme common to all of them, reminiscent of Mumford and van Moerbeke’s treatment of the Toda lattice, and prove the independence of the linearization on the representation. The paper also contains a beautiful appendix in which the authors sketch the main concepts and theorems of the theory of correspondence in a style reminiscent of the classic Italian geometers.

MSC:
37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
53D50 Geometric quantization
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
14E05 Rational and birational maps
14H40 Jacobians, Prym varieties
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