Classification of almost spherical pairs of compact simple Lie groups

Ihor Mykytyuk; Anatoly Stepin

Banach Center Publications (2000)

  • Volume: 51, Issue: 1, page 231-241
  • ISSN: 0137-6934

Abstract

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All homogeneous spaces G/K (G is a simple connected compact Lie group, K a connected closed subgroup) are enumerated for which arbitrary Hamiltonian flows on T*(G/K) with G-invariant Hamiltonians are integrable in the class of Noether integrals and G-invariant functions.

How to cite

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Mykytyuk, Ihor, and Stepin, Anatoly. "Classification of almost spherical pairs of compact simple Lie groups." Banach Center Publications 51.1 (2000): 231-241. <http://eudml.org/doc/209035>.

@article{Mykytyuk2000,
abstract = {All homogeneous spaces G/K (G is a simple connected compact Lie group, K a connected closed subgroup) are enumerated for which arbitrary Hamiltonian flows on T*(G/K) with G-invariant Hamiltonians are integrable in the class of Noether integrals and G-invariant functions.},
author = {Mykytyuk, Ihor, Stepin, Anatoly},
journal = {Banach Center Publications},
keywords = {simple connected compact Lie group; symplectic manifold; moment map; spherical pairs},
language = {eng},
number = {1},
pages = {231-241},
title = {Classification of almost spherical pairs of compact simple Lie groups},
url = {http://eudml.org/doc/209035},
volume = {51},
year = {2000},
}

TY - JOUR
AU - Mykytyuk, Ihor
AU - Stepin, Anatoly
TI - Classification of almost spherical pairs of compact simple Lie groups
JO - Banach Center Publications
PY - 2000
VL - 51
IS - 1
SP - 231
EP - 241
AB - All homogeneous spaces G/K (G is a simple connected compact Lie group, K a connected closed subgroup) are enumerated for which arbitrary Hamiltonian flows on T*(G/K) with G-invariant Hamiltonians are integrable in the class of Noether integrals and G-invariant functions.
LA - eng
KW - simple connected compact Lie group; symplectic manifold; moment map; spherical pairs
UR - http://eudml.org/doc/209035
ER -

References

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  2. [Bo1] N. Bourbaki, Lie groups and algebras, I-III, Mir, Moscow, 1970 (in Russian). 
  3. [Bo2] N. Bourbaki, Lie groups and algebras, IV-VI, Mir, Moscow, 1972 (in Russian). 
  4. [Bo3] N. Bourbaki, Lie groups and algebras, VII,VIII, Mir, Moscow, 1978 (in Russian). 
  5. [Br] M. Brion, Classification des espaces homogenes spheriques, Compositio Math. 63 (1987), 189-208. 
  6. [Ch] M. L. Chumak, Integrable G-invariant Hamiltonian systems and uniform spaces with simple spectrum, Func. Anal. and its Applic. 20 (1986), 91-92. 
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  8. [Dy2] E. B. Dynkin, Semisimple subalgebras of semisimple Lie algebras, Matem. Sbornik 30 (1952), 349-462 (in Russian); Am. Math. Soc. Transl. 2 (1957), 111-244. Zbl0048.01701
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  10. [GG] M. Goto and F. Grosshans, Semisimple Lie algebras, Vol. 38, Lecture Notes in Pure and Applied Math., New York and Basel, 1978. Zbl0391.17004
  11. [GS1] V. Guillemin and S. Sternberg, Multiplicity-free spaces, J. Differential Geometry 19 (1984), 31-56. Zbl0548.58017
  12. [GS2] V. Guillemin and S. Sternberg, On collective complete integrability according to the method of Thimm, Ergod. Theory and Dynam. Syst. 3 (1983), 219-230. Zbl0511.58024
  13. [GS3] V. Guillemin and S. Sternberg, Geometric asymptotics, AMS, Providence, Rhode Island, 1977. 
  14. [He] S. Helgason, Differential geometry and symmetric spaces, Academic Press, 1962. Zbl0111.18101
  15. [IW] K. Ii and S. Watanabe, Complete integrability of the geodesic flows on symmetric spaces, in: Geometry of Geodesics and Related Topics, Tokyo, K. Shiohama (ed.), North-Holland, 1984, 105-124. 
  16. [Kr] M. Kramer, Sphärische Untergruppen in kompakten zusammenhängenden Liegruppen, Compositio Math. 38 (1979), 129-153. Zbl0402.22006
  17. [Mi] A. S. Mishchenko, Integration of geodesic flows on symmetric spaces, Mat. Zametki 32 (1982), 257-262 (in Russian). Zbl0487.58010
  18. [My1] I. V. Mykytiuk, Homogeneous spaces with integrable G-invariant Hamiltonian flows, Math. USSR Izvestiya 23 (1984), 511-523. 
  19. [My2] I. V. Mykytiuk, On the integrability of invariant Hamiltonian systems with homogeneous configuration spaces, Math. USSR Sbornik 57 (1987), 527-546. 
  20. [On] A. L. Onishchik, Inclusion relations between transitive compact transformation groups, Trudy Mosc. Matem. Obshchestva 11 (1962), 199-242 (in Russian). Zbl0192.12601
  21. [PM] A. K. Prykarpatsky and I. V. Mykytiuk, Algebraic integrability of nonlinear dynamical systems on manifolds. Classical and quantum aspects, Vol. 443, Math. and its Appl., Kluwer Academic Publishers, 1998. Zbl0937.37055
  22. [Ti] A. Timm, Integrable geodesic flows on homogeneous spaces, Ergod. Theory and Dynam. Syst. 1 (1981), 495-517. 

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