The full symmetric Toda flow and intersections of Bruhat cells

DOI10.3842/SIGMA.2020.115zbMath1471.17022arXiv1810.09622MaRDI QIDQ2217973

Yuri B. Chernyakov, Dmitry Talalaev, Georgy I. Sharygin, Alexander S. Sorin

Publication date: 12 January 2021

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1810.09622

zbMATH Keywords

Lie groupsintegrable systemsBruhat orderToda flow

Mathematics Subject Classification ID

Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06) General properties and structure of real Lie groups (22E15) Simple, semisimple, reductive (super)algebras (17B20)

Cites Work

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• Bruhat order in the Toda system on \(\mathfrak{so}(2, 4)\): an example of non-split real form
• On some geometric aspects of Bruhat orderings. I: A finer decomposition of Bruhat cells
• Completely integrable gradient flows
• Hamiltonian and gradient structures in the Toda flows
• Toda flows and real Hessenberg manifolds
• Phase portraits of the full symmetric Toda systems on rank-2 groups
• Toda lattice, cohomology of compact Lie groups and finite Chevalley groups
• Bruhat order in full symmetric Toda system
• Toda Flows and Isospectral Manifolds

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