Linearization of Hamiltonian systems, Jacobi varieties and representation theory
type: Item
instance of: scholarly article
title: Linearization of Hamiltonian systems, Jacobi varieties and representation theory
zbMATH Open document ID: 0455.58010
DOI: 10.1016/0001-8708(80)90008-0
author: Mark Adler
author: Pierre van Moerbeke
published in: Advances in Mathematics
publication date: 1980-01-01T00:00:00Z
review text: 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.
reviewed by: Mircea Puta
Mathematics Subject Classification ID: 37J35
Mathematics Subject Classification ID: 53D50
Mathematics Subject Classification ID: 17B10
Mathematics Subject Classification ID: 14E05
Mathematics Subject Classification ID: 14H40
zbMATH DE Number: 3712863
zbMATH Keywords: Toda type flow
zbMATH Keywords: flows of spinning top type
zbMATH Keywords: Lie algebra representation
zbMATH Keywords: theory of correspondences
zbMATH Keywords: linearization of Hamiltonian system
zbMATH Keywords: Jacobi varieties
zbMATH Keywords: representation theory
zbMATH Keywords: algebraic curve
zbMATH Keywords: Kac-Moody algebras
MaRDI profile type: Publication
full work available at URL: 0001-8708(80)90008-0
OpenAlex ID: W2023620134
cites work: On a trace functional for formal pseudo-differential operators and the symplectic structure of the Korteweg-deVries type equations
cites work: Completely integrable systems, Euclidean Lie algebras, and curves
cites work: The Jacobian Variety of an Algebraic Curve
cites work: Q3256658
cites work: Fibre Systems of Jacobian Varieties
cites work: The spectrum of Hill's equation
cites work: Hill and toda curves
cites work: Q5816366
cites work: Specialization of Cycles on a Projective Model
cites work: The spectrum of Jacobi matrices
cites work: Q3915684
cites work: The spectrum of difference operators and algebraic curves
cites work: Q3874985
cites work: Q3870362
cites work: Reduction of Algebraic Varieties with Respect to a Discrete Valuation of the Basic Field
cites work: Q5609066
cites work: Q4167627
cites work: Transversal Homoclinic Orbits in an Integrable System
cites work: Secant Bundles on Symmetric Products
cites work: Reduction of Hamiltonian systems, affine Lie algebras and Lax equations
description: scientific article; zbMATH DE number 3712863