Action-angle coordinates on coadjoint orbits and multiplicity free spaces from partial tropicalization

DOI10.1016/j.aim.2022.108856OpenAlexW3013770983MaRDI QIDQ2685676

Benjamin Hoffman, Anton Yu. Alekseev, Jeremy Lane, Yanpeng Li

Publication date: 22 February 2023

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2003.13621

zbMATH Keywords

symplectic geometryPoisson-Lie groupscoadjoint orbitsHamiltonian group actionsfree spaces

Mathematics Subject Classification ID

Symplectic manifolds (general theory) (53D05) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Poisson manifolds; Poisson groupoids and algebroids (53D17) Coadjoint orbits; nilpotent varieties (17B08) Applications of tropical geometry (14T90) General theory of finite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, invariants (37J06) Relations of finite-dimensional Hamiltonian and Lagrangian systems with topology, geometry and differential geometry (symplectic geometry, Poisson geometry, etc.) (37J39) Relations of finite-dimensional Hamiltonian and Lagrangian systems with Lie algebras and other algebraic structures (37J37)

Related Items (1)

Canonical domains for coadjoint orbits

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The symplectic geometry of polygons in Euclidean space
• Gromov width of non-regular coadjoint orbits of \(\mathrm{U}(n)\), \(\mathrm{SO}(2n)\) and \(\mathrm{SO}(2n + 1)\)
• Multiplicity-free spaces
• Non-compact symplectic toric manifolds
• Integrable systems, toric degenerations and Okounkov bodies
• Crystal bases and Newton-Okounkov bodies
• Graded cluster algebras
• The quantum dilogarithm and representations of quantum cluster varieties
• The Gelfand-Cetlin system and quantization of the complex flag manifolds
• Pseudo holomorphic curves in symplectic manifolds
• Poisson Lie groups, dressing transformations, and Bruhat decompositions
• The moment map and collective motion
• Real polarization of the moduli space of flat connections on a Riemann surface
• On Poisson actions of compact Lie groups on symplectic manifolds
• Multiplicity-free Hamiltonian actions need not be Kähler
• Classical dynamical \(r\)-matrices and homogeneous Poisson structures on \(G/H\) and \(K/T\)
• Tensor product multiplicities, canonical and totally positive varieties
• Toric degenerations of Schubert varieties
• Symplectic implosion
• Quantum groups, quantum tori, and the Grothendieck-Springer resolution
• Cluster algebras. III: Upper bounds and double Bruhat cells.
• Toric degenerations of spherical varieties
• Langlands duality and Poisson-Lie duality via cluster theory and tropicalization
• Concentration of symplectic volumes on Poisson homogeneous spaces
• Poisson structures and potentials
• The Gromov width of complex Grassmannians
• Heckman, Kostant, and Steinberg formulas for symplectic manifolds
• Upper bound for the Gromov width of coadjoint orbits of compact Lie groups
• Lie-Poisson Structure on Some Poisson Lie Groups
• Double Bruhat cells and total positivity
• Contraction of Hamiltonian $K$-Spaces
• The U ( n ) Gelfand–Zeitlin system as a tropical limit of Ginzburg–Weinstein diffeomorphisms
• Simplices in Newton–Okounkov bodies and the Gromov width of coadjoint orbits
• Duals of Semisimple Poisson–Lie Groups and Cluster Theory of Moduli Spaces of G-local Systems
• Periodic Staircase Matrices and Generalized Cluster Structures
• On toric degenerations of flag varieties
• Automorphisms of multiplicity free Hamiltonian manifolds
• Quantum cluster algebra structures on quantum nilpotent algebras
• Linearization of Poisson actions and singular values of matrix products

This page was built for publication: Action-angle coordinates on coadjoint orbits and multiplicity free spaces from partial tropicalization