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
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)
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Cites Work
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- 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
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