Geodesic
A~bi-Hamiltonian system on the~Grassmannian
Teoretičeskaâ i matematičeskaâ fizika, Tome 189 (2016) no. 1, pp. 3-14

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Considering the recent result that the Poisson–Nijenhuis geometry corresponds to the quantization of the symplectic groupoid integrating a Poisson manifold, we discuss the Poisson–Nijenhuis structure on the Grassmannian defined by the compatible Kirillov–Kostant–Souriau and Bruhat–Poisson structures. The eigenvalues of the Nijenhuis tensor are Gelfand–Tsetlin variables, which, as was proved, are also in involution with respect to the Bruhat–Poisson structure. Moreover, we show that the Stiefel bundle on the Grassmannian admits a bi-Hamiltonian structure.
Keywords: symplectic geometry, integrable system, Poisson–Nijenhuis geometry, symplectic groupoid.
Mots-clés : Poisson manifold quantization 
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     author = {F. Bonechi and J. Qiu and M. Tarlini},
     title = {A~bi-Hamiltonian system on {the~Grassmannian}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     year = {2016},
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     url = {http://geodesic.mathdoc.fr/item/TMF_2016_189_1_a0/}
}
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F. Bonechi; J. Qiu; M. Tarlini. A~bi-Hamiltonian system on the~Grassmannian. Teoretičeskaâ i matematičeskaâ fizika, Tome 189 (2016) no. 1, pp. 3-14. http://geodesic.mathdoc.fr/item/TMF_2016_189_1_a0/