Geodesic
On the integrability of invariant Hamiltonian systems with homogeneous configuration spaces
Sbornik. Mathematics, Tome 57 (1987) no. 2, pp. 527-546

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All homogeneous spaces $G/K$ ($G$ is a semisimple complex (compact) Lie group, $K$ a reductive subgroup) are enumerated for which arbitrary Hamiltonian flows on $T^*(G/K)$ with $G$-invariant Hamiltonians are integrable in the class of Noether integrals. It is proved that only for these spaces $G/K$ does the quasiregular representation of $G$ in the space of regular functions of the algebraic variety $G/K$ have a simple spectrum. Bibliography: 21 titles. 
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     author = {I. V. Mykytyuk},
     title = {On the integrability of invariant {Hamiltonian} systems with homogeneous configuration spaces},
     journal = {Sbornik. Mathematics},
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     volume = {57},
     number = {2},
     year = {1987},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1987_57_2_a13/}
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I. V. Mykytyuk. On the integrability of invariant Hamiltonian systems with homogeneous configuration spaces. Sbornik. Mathematics, Tome 57 (1987) no. 2, pp. 527-546. http://geodesic.mathdoc.fr/item/SM_1987_57_2_a13/