Limit matrices for the Toda flow and periodic flags for loop groups

DOI10.1007/BF01445092zbMath0788.58028OpenAlexW1999675821MaRDI QIDQ1318096

Luc Haine, Mark Adler, Pierre van Moerbeke

Publication date: 26 April 1994

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/165072

zbMATH Keywords

isospectral manifoldsperiodic Jacobi matricesToda flowsperiodic flag manifolds

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Loop groups and related constructions, group-theoretic treatment (22E67) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35)

Related Items

Stratifications of hyperelliptic Jacobians and the Sato Grassmannian, Infinite-dimensional flag manifolds in integrable systems, Integrable systems and supersymmetric gauge theory, Quasi-periodic and periodic solutions of the Toda lattice via the hyperelliptic sigma function, BREAKING OF LINEAR SYMMETRIES AND MICHEL'S THEORY: GRASSMANN MANIFOLDS, AND INVARIANT SUBSPACES, Integrable systems for \(\overline\partial\) operators of non-zero index, The Toda lattice, Dynkin diagrams, singularities and Abelian varieties, Singular sector of the Kadomtsev–Petviashvili hierarchy, ∂̄ operators of nonzero index, and associated integrable systems, The monoidal transformation by Painlevé divisor and resolution of the poles of the Toda lattice, An algebraic characterization of the bilinear relations of the matrix hierarchy associated with a commutative algebra of \(k\times k\)-matrices, Nonlinear superposition formulas based on imprimitive group action, On the inverse eigenvalue problem for periodic Jacobi matrices, Generalized inverse eigenvalue problems for augmented periodic Jacobi matrices, Hidden hierarchies of KdV type on Birkhoff strata

Cites Work

• Loop groups and equations of KdV type
• Classical and quantum mechanical systems of Toda-lattice type. II: Solutions of the classical flows
• The solution to a generalized Toda lattice and representation theory
• Completely integrable systems, Euclidean Lie algebras, and curves
• Kowalewski's asymptotic method, Kac-Moody Lie algebras and regularization
• The spectrum of difference operators and algebraic curves
• Variétés de drapeaux et réseaux de Toda. (Flag manifolds and Toda lattices)
• Birkhoff strata, Bäcklund transformations, and regularization of isospectral operators
• Operator Approach to the Kadomtsev-Petviashvili Equation–Transformation Groups for Soliton Equations III–
• Tata lectures on theta. II: Jacobian theta functions and differential equations. With the collaboration of C. Musili, M. Nori, E. Previato, M. Stillman, and H. Umemura
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