The Toda flows preserving small cells of the flag variety \(G/B\) and Kazhdan's \(x_{0}\)-grading

DOI10.1016/j.geomphys.2006.06.003zbMath1106.37046OpenAlexW1964281013MaRDI QIDQ864837

Kaoru Ikeda

Publication date: 13 February 2007

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.geomphys.2006.06.003

zbMATH Keywords

Toda latticeBruhat decompositionGauss decompositionKostant-Toda lattice

Mathematics Subject Classification ID

Special varieties (14M99) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Lattice dynamics; integrable lattice equations (37K60)

Related Items (1)

The monoidal transformation by Painlevé divisor and resolution of the poles of the Toda lattice

Cites Work

• The topology of isospectral manifolds of tridiagonal matrices
• Compactifications of the iso level sets of the Hessenberg matrices and the full Kostant-Toda lattice
• A new integrable case of the motion of the 4-dimensional rigid body
• The solution to a generalized Toda lattice and representation theory
• Variétés de drapeaux et réseaux de Toda. (Flag manifolds and Toda lattices)
• On Whittaker vectors and representation theory
• Regularization of Toda lattices by Hamiltonian reduction
• On the geometry of certain isospectral sets in the full Kostant-Toda lattice
• Toda lattice and toric varieties for real split semisimple Lie algebras.
• Iso-spectral deformations of general matrix and their reductions on Lie algebras
• The toda flow on a generic orbit is integrable
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