Integrability of characteristic Hamiltonian systems on simple Lie groups with standard Poisson Lie structure

DOI10.1007/s00220-003-0916-3zbMath1078.37043arXivmath/0103147OpenAlexW2061167526WikidataQ115388691 ScholiaQ115388691MaRDI QIDQ1416939

Nicolai Reshetikhin

Publication date: 16 December 2003

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0103147

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Poisson manifolds; Poisson groupoids and algebroids (53D17) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06)

Related Items

Degenerately integrable systems, Double Bruhat cells in Kac-Moody groups and integrable systems, Superintegrability of Generalized Toda Models on Symmetric Spaces, Lie algebraic aspects of the finite nonperiodic Toda flows, Macdonald duality and the proof of the quantum Q-system conjecture, Cluster ensembles and Kac-Moody groups, Generalized Bäcklund-Darboux transformations for Coxeter-Toda flows from a cluster algebra perspective, A non-local Poisson bracket for Coxeter--Toda lattices, Cluster $\mathcal X$-varieties for dual Poisson–Lie groups. I, Superintegrable systems on moduli spaces of flat connections

Cites Work

• The solution to a generalized Toda lattice and representation theory
• Systems of Toda type, inverse spectral problems, and representation theory
• On a trace functional for formal pseudo-differential operators and the symplectic structure of the Korteweg-deVries type equations
• Reduction of Hamiltonian systems, affine Lie algebras and Lax equations
• Primitive ideals of \({\mathbf C}_ q[SL(3)\)]
• The SVD flows on generic symplectic leaves are completely integrable
• Factorization dynamics and Coxeter-Toda lattices
• The toda flow on a generic orbit is integrable
• Double Bruhat cells and total positivity
• Dressing transformations and Poisson group actions
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item