A convexity theorem for Poisson actions of compact Lie groups

DOI10.24033/asens.1754zbMath0877.58025OpenAlexW1561928413WikidataQ115228355 ScholiaQ115228355MaRDI QIDQ4338375

Tudor S. Ratiu, Hermann Flaschka

Publication date: 8 December 1997

Published in: Annales scientifiques de l'École normale supérieure (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=ASENS_1996_4_29_6_787_0

zbMATH Keywords

convexityPoisson Lie groupmomentum mapping

Mathematics Subject Classification ID

Related Items (20)

Convexity and Thimm's trick ⋮ Completeness of determinantal Hamiltonian flows on the matrix affine Poisson space ⋮ Super Poisson-Lie structure on \(\text{SU}(mn)\) via \(\text{SL}(m|n, \mathbb C)^{\mathbb R}\) ⋮ Convexity of Singular Affine Structures and Toric-Focus Integrable Hamiltonian Systems ⋮ Hyperbolic spin Ruijsenaars-Schneider model from Poisson reduction ⋮ Dirac actions and Lu's Lie algebroid ⋮ A new integral formula for Heckman-Opdam hypergeometric functions ⋮ Hamiltonian and symplectic symmetries: An introduction ⋮ Lagrangian fibers of Gelfand-Cetlin systems of \(\mathrm{SO}(n)\)-type ⋮ Symplectic invariants of semitoric systems and the inverse problem for quantum systems ⋮ Singular fibres of the Gelfand–Cetlin system on MANI( n )* ⋮ Symplectic convexity for orbifolds ⋮ Openness and convexity for momentum maps ⋮ Linearization of Poisson actions and singular values of matrix products ⋮ Inequalities from Poisson brackets ⋮ Symplectic theory of completely integrable Hamiltonian systems ⋮ The Poisson geometry of SU(1,1) ⋮ Momentum maps and reduction in algebraic geometry ⋮ ON MOMENT MAPS ASSOCIATED TO A TWISTED HEISENBERG DOUBLE ⋮ Proper groupoids and momentum maps: Linearization, affinity, and convexity

Cites Work

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• Algebras of functions on compact quantum groups, Schubert cells and quantum tori
• Poisson Lie groups, dressing transformations, and Bruhat decompositions
• Symmetry and bifurcations of momentum mappings
• Convexity properties of the moment mapping
• Convexity properties of the moment mapping. II
• Convexity properties of the moment mapping. III
• Differenzierbare G-Mannigfaltigkeiten
• Convexity and Commuting Hamiltonians
• On the Nonlinear Convexity Theorem of Kostant
• Inequalities: theory of majorization and its applications

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