Variétés de drapeaux et réseaux de Toda. (Flag manifolds and Toda lattices)

DOI10.1007/BF02571544zbMath0744.58031MaRDI QIDQ1189273

Luc Haine, Hermann Flaschka

Publication date: 26 September 1992

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

Full work available at URL: https://eudml.org/doc/174335

zbMATH Keywords

flag manifoldToda latticeBruhat cellssemisimple complex Lie algebra

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Grassmannians, Schubert varieties, flag manifolds (14M15) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Simple, semisimple, reductive (super)algebras (17B20)

Related Items

Rational functions, Toda flows, and LR-like algorithms, Regularization of Toda lattices by Hamiltonian reduction, The Toda flows preserving small cells of the flag variety \(G/B\) and Kazhdan's \(x_{0}\)-grading, Singular structure of Toda lattices and cohomology of certain compact Lie groups, Compactifications of the iso level sets of the Hessenberg matrices and the full Kostant-Toda lattice, Extensions of the finite nonperiodic Toda lattices with indefinite metrics, A path-counting analysis of phase shifts in box-ball systems, Extended Schur's \(Q\)-functions and the full Kostant-Toda hierarchy on the Lie algebra of type \(D\), The monoidal transformation by Painlevé divisor and resolution of the poles of the Toda lattice, On stable solutions of the finite non-periodic Toda lattice, The full Kostant-Toda hierarchy on the positive flag variety, Toda lattice, cohomology of compact Lie groups and finite Chevalley groups, Fifty years of the finite nonperiodic Toda lattice: a geometric and topological viewpoint, Toda lattices with indefinite metric. II: Topology of the iso-spectral manifolds, The resolutions of the singular loci of the Toda lattice on the split and connected reductive Lie groups, Limit matrices for the Toda flow and periodic flags for loop groups

Cites Work

• Unnamed Item
• Unnamed Item
• Integrable Hamiltonian systems connected with graded Lie algebras
• 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
• The Toda lattice, Dynkin diagrams, singularities and Abelian varieties
• Torus orbits in \(G/P\)
• On Whittaker vectors and representation theory
• The Principal Three-Dimensional Subgroup and the Betti Numbers of a Complex Simple Lie Group
• The toda flow on a generic orbit is integrable
• Combinatorial geometries and torus strata on homogeneous compact manifolds
• SCHUBERT CELLS AND COHOMOLOGY OF THE SPACESG/P
• Lie Group Representations on Polynomial Rings
• Explicit solutions of classical generalized Toda models