@article{ASENS_1996_4_29_6_787_0, author = {Flaschka, Hermann and Ratiu, Tudor}, title = {A convexity theorem for Poisson actions of compact Lie groups}, journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure}, volume = {29}, year = {1996}, pages = {787-809}, doi = {10.24033/asens.1754}, mrnumber = {98a:58068}, zbl = {0877.58025}, language = {en}, url = {http://dml.mathdoc.fr/item/ASENS_1996_4_29_6_787_0} }
Flaschka, Hermann; Ratiu, Tudor. A convexity theorem for Poisson actions of compact Lie groups. Annales scientifiques de l'École Normale Supérieure, Tome 29 (1996) pp. 787-809. doi : 10.24033/asens.1754. http://gdmltest.u-ga.fr/item/ASENS_1996_4_29_6_787_0/
[AMM] Symmetries and bifurcations of the momentum mapping (Comm. Math. Phys., Vol. 78, 1981, pp. 455-478). | MR 82m:58028 | Zbl 0486.58008
, and ,[A] Convexity and commuting Hamiltonians (Bull. London Math. Soc., Vol. 14, 1982, pp. 1-15). | MR 83e:53037 | Zbl 0482.58013
,[Br] Introduction to Compact Transformation Groups, Academic Press, New York and London, 1972. | MR 54 #1265 | Zbl 0246.57017
,[CK] Convexity of the moment map for nonabelian compact groups ; a proof by M. CONDEVAUX, P. DAZORD and P. MOLINO (Unpublished lecture notes, MIT, February 1991).
and ,[CDM] Géométrie du moment, in Séminaire Sud-Rhodanien, Lyon, 1988. | MR 1040871
, and ,[GS1] Convexity properties of the momentum mapping I (Invent. Math., Vol. 67, 1982, pp. 491-513). | MR 83m:58037 | Zbl 0503.58017
and ,[GS2] Convexity properties of the momentum mapping II (Invent. Math., Vol. 77, 1984, pp. 533-546). | MR 86b:58042a | Zbl 0561.58015
and ,[He] Differential Geometry, Lie Groups, and Symmetric Spaces, Academic Press, New York, 1978. | MR 80k:53081 | Zbl 0451.53038
,[HNP] Symplectic convexity theorems and coadjoint orbits (Comp. Math., Vol. 94, 1994, pp. 129-180). | Numdam | MR 96d:53053 | Zbl 0819.22006
, and ,[J] Differenzierbare G-Mannigfaltigkeiten (Lecture Notes in Math., Vol. 59, 1968, Springer-Verlag). | MR 37 #4835 | Zbl 0159.53701
,[Ka] Perturbation Theory for Linear Operators (Die Grundlehren der Mathematischen Wissenschaften, Vol. 132, Springer Verlag, New York-Berlin-Heidelberg, 1966). | MR 34 #3324 | Zbl 0148.12601
,[Ki] Convexity properties of the momentum mapping III (Invent. Math., Vol. 77, 1984, pp. 547-552). | MR 86b:58042b | Zbl 0561.58016
,[LS] Algebras of functions on compact quantum groups, Schubert cells and quantum tori (Comm. Math. Phys. Vol. 139, 1991, pp. 141-170). | MR 92h:58020 | Zbl 0729.17011
and ,[Lu1] Multiplicative and Affine Poisson Structures on Lie Groups, (Ph. D. dissertation, University of California at Berkeley, 1990).
,[Lu2] 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] On the nonlinear convexity theorem of Kostant (J. A.M.S., Vol. 4, 1991, pp. 349-363). | MR 92a:58048 | Zbl 0785.22019
and ,[LuWe] Poisson Lie groups, dressing transformations, and Bruhat decompositions, (J. Diff. Geom., Vol. 31, 1990, pp. 510-526). | MR 91c:22012 | Zbl 0673.58018
and ,[MO] Inequalities : Theory of Majorization and its Applications, Academic Press, New York, 1979. | MR 81b:00002 | Zbl 0437.26007
and ,