A convexity theorem for Poisson actions of compact Lie groups
Annales scientifiques de l'École Normale Supérieure (1996)
- Volume: 29, Issue: 6, page 787-809
- ISSN: 0012-9593
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topFlaschka, Hermann, and Ratiu, Tudor. "A convexity theorem for Poisson actions of compact Lie groups." Annales scientifiques de l'École Normale Supérieure 29.6 (1996): 787-809. <http://eudml.org/doc/82423>.
@article{Flaschka1996,
author = {Flaschka, Hermann, Ratiu, Tudor},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {Poisson Lie group; momentum mapping; convexity},
language = {eng},
number = {6},
pages = {787-809},
publisher = {Elsevier},
title = {A convexity theorem for Poisson actions of compact Lie groups},
url = {http://eudml.org/doc/82423},
volume = {29},
year = {1996},
}
TY - JOUR
AU - Flaschka, Hermann
AU - Ratiu, Tudor
TI - A convexity theorem for Poisson actions of compact Lie groups
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1996
PB - Elsevier
VL - 29
IS - 6
SP - 787
EP - 809
LA - eng
KW - Poisson Lie group; momentum mapping; convexity
UR - http://eudml.org/doc/82423
ER -
References
top- [AMM] J. ARMS, J. E. MARSDEN and V. MONCRIEF, Symmetries and bifurcations of the momentum mapping (Comm. Math. Phys., Vol. 78, 1981, pp. 455-478). Zbl0486.58008MR82m:58028
- [A] M. F. ATIYAH, Convexity and commuting Hamiltonians (Bull. London Math. Soc., Vol. 14, 1982, pp. 1-15). Zbl0482.58013MR83e:53037
- [Br] G. E. BREDON, Introduction to Compact Transformation Groups, Academic Press, New York and London, 1972. Zbl0246.57017MR54 #1265
- [CK] S. CHEMLA and Y. KARSHON, Convexity of the moment map for nonabelian compact groups ; a proof by M. CONDEVAUX, P. DAZORD and P. MOLINO (Unpublished lecture notes, MIT, February 1991).
- [CDM] M. CONDEVAUX, P. DAZORD and P. MOLINO, Géométrie du moment, in Séminaire Sud-Rhodanien, Lyon, 1988. MR1040871
- [GS1] V. GUILLEMIN and S. STERNBERG, Convexity properties of the momentum mapping I (Invent. Math., Vol. 67, 1982, pp. 491-513). Zbl0503.58017MR83m:58037
- [GS2] V. GUILLEMIN and S. STERNBERG, Convexity properties of the momentum mapping II (Invent. Math., Vol. 77, 1984, pp. 533-546). Zbl0561.58015MR86b:58042a
- [He] S. HELGASON, Differential Geometry, Lie Groups, and Symmetric Spaces, Academic Press, New York, 1978. Zbl0451.53038MR80k:53081
- [HNP] J. HILGERT, K.-H. NEEB and W. PLANK, Symplectic convexity theorems and coadjoint orbits (Comp. Math., Vol. 94, 1994, pp. 129-180). Zbl0819.22006MR96d:53053
- [J] K. JÄNICH, Differenzierbare G-Mannigfaltigkeiten (Lecture Notes in Math., Vol. 59, 1968, Springer-Verlag). Zbl0159.53701MR37 #4835
- [Ka] T. KATO, Perturbation Theory for Linear Operators (Die Grundlehren der Mathematischen Wissenschaften, Vol. 132, Springer Verlag, New York-Berlin-Heidelberg, 1966). Zbl0148.12601MR34 #3324
- [Ki] F. C. KIRWAN, Convexity properties of the momentum mapping III (Invent. Math., Vol. 77, 1984, pp. 547-552). Zbl0561.58016MR86b:58042b
- [LS] S. LEVENDORSKIĬ and Y. SOIBELMAN, Algebras of functions on compact quantum groups, Schubert cells and quantum tori (Comm. Math. Phys. Vol. 139, 1991, pp. 141-170). Zbl0729.17011MR92h:58020
- [Lu1] J.-H. LU, Multiplicative and Affine Poisson Structures on Lie Groups, (Ph. D. dissertation, University of California at Berkeley, 1990).
- [Lu2] J.-H. LU, Momentum mappings and reduction of Poisson actions, in Proc. of the Sém. Sud-Rhodanien de Géométrie at Berkeley, 1989, Springer Verlag MSRI Series, 1991.
- [LuRa] J.-H. LU and T. RATIU, On the nonlinear convexity theorem of Kostant (J. A.M.S., Vol. 4, 1991, pp. 349-363). Zbl0785.22019MR92a:58048
- [LuWe] J.-H. LU and A. WEINSTEIN, Poisson Lie groups, dressing transformations, and Bruhat decompositions, (J. Diff. Geom., Vol. 31, 1990, pp. 510-526). Zbl0673.58018MR91c:22012
- [MO] A. W. MARSHALL and I. OLKIN, Inequalities : Theory of Majorization and its Applications, Academic Press, New York, 1979. Zbl0437.26007MR81b:00002
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