On rational symplectic parametrization of the coadjoint orbit of $\mathrm{GL}(N)$. Diagonalizable case

DOI10.1090/S1061-0022-2011-01145-8zbMath1222.53080MaRDI QIDQ3013545

Mikhail Vasilievich Babich, Sergey E. Derkachov

Publication date: 18 July 2011

Published in: St. Petersburg Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

coadjoint orbitPoisson bracketsymplectic formrationalityDarboux coordinates

Mathematics Subject Classification ID

Symplectic manifolds (general theory) (53D05) Coadjoint orbits; nilpotent varieties (17B08)

Related Items (4)

Birational Darboux coordinates on (co)adjoint orbits of \(\mathrm{GL}(N,\mathbb{C})\) ⋮ Regular representation of the group \(\mathrm{GL}(N, \mathbb{R})\): factorization, Casimir operators and Toda chain ⋮ Isomonodromic deformations: confluence, reduction and quantisation ⋮ On birational Darboux coordinates on coadjoint orbits of classical complex Lie groups

Cites Work

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• About coordinates on the phase spaces of the Schlesinger system and the Garnier-Painlevé 6 system
• Quantization of symplectic orbits of compact Lie groups by means of the functional integral
• Rational symplectic coordinates on the space of Fuchs equations \(m \times m\)-case
• Reduction of symplectic manifolds with symmetry
• Geometrical aspects of Schlesinger's equation
• \(\mathcal R\)-matrix and Baxter \(\mathcal Q\)-operators for the noncompact \(\mathrm{SL}(N,\mathbb C)\) invariant spin chain
• Canonical structure and symmetries of the Schlesinger equations

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