The U ( n ) Gelfand–Zeitlin system as a tropical limit of Ginzburg–Weinstein diffeomorphisms

DOI10.1098/rsta.2017.0428zbMath1407.53092arXiv1804.01504OpenAlexW3105455508WikidataQ91493167 ScholiaQ91493167MaRDI QIDQ4626215

Yanpeng Li, Jeremy Lane, Anton Yu. Alekseev

Publication date: 27 February 2019

Published in: Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1804.01504

zbMATH Keywords

integrable systemsPoisson-Lie groupstropicalizationPoisson geometryGelfand-Zeitlin

Mathematics Subject Classification ID

Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06) Geodesic flows in symplectic geometry and contact geometry (53D25)

Related Items

Action-angle coordinates on coadjoint orbits and multiplicity free spaces from partial tropicalization ⋮ Lagrangian fibers of Gelfand-Cetlin systems of \(\mathrm{SO}(n)\)-type ⋮ Local normal forms for multiplicity free \(U(n)\) actions on coadjoint orbits ⋮ Langlands duality and Poisson-Lie duality via cluster theory and tropicalization

Cites Work

• Unnamed Item
• Gromov width of non-regular coadjoint orbits of \(\mathrm{U}(n)\), \(\mathrm{SO}(2n)\) and \(\mathrm{SO}(2n + 1)\)
• Inequalities from Poisson brackets
• Ginzburg-Weinstein via Gelfand-Zeitlin
• Integrable systems, toric degenerations and Okounkov bodies
• Toric degenerations of Gelfand-Cetlin systems and potential functions
• The Gelfand-Cetlin system and quantization of the complex flag manifolds
• Normal forms for smooth Poisson structures
• The moment map and collective motion
• On Poisson actions of compact Lie groups on symplectic manifolds
• Tensor product multiplicities, canonical and totally positive varieties
• Stokes matrices, Poisson Lie groups and Frobenius manifolds.
• Cluster algebras. III: Upper bounds and double Bruhat cells.
• The Horn problem and planar networks
• A symplectic proof of the Horn inequalities
• Cluster algebras I: Foundations
• Comparison of Poisson structures and Poisson-Lie dynamical r-matrices
• Integrable geodesic flows on homogeneous spaces
• Lie-Poisson Structure on Some Poisson Lie Groups
• EULER EQUATIONS ON FINITE-DIMENSIONAL LIE GROUPS
• On collective complete integrability according to the method of Thimm
• Dressing transformations and Poisson group actions
• Total positivity: tests and parametrizations.