Skip to Main Content

Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

On the nonlinear convexity theorem of Kostant
HTML articles powered by AMS MathViewer

by Jiang-Hua Lu and Tudor Ratiu PDF
J. Amer. Math. Soc. 4 (1991), 349-363 Request permission
References
  • M. F. Atiyah, Convexity and commuting Hamiltonians, Bull. London Math. Soc. 14 (1982), no. 1, 1–15. MR 642416, DOI 10.1112/blms/14.1.1
  • Jack F. Conn, Normal forms for smooth Poisson structures, Ann. of Math. (2) 121 (1985), no. 3, 565–593. MR 794374, DOI 10.2307/1971210
  • C. de Concini and V. G. Kac, Representations of quantum groups at roots of 1, Operator Algebras, Unitary Representations, Enveloping Algebras, and Invariant Theory, Actes du Colloque en l’honneur de Jacques Dixmier (A. Connes, M. Duflo, A. Joseph, and R. Rentschter, eds.), Progr. Math., Birkhäuser, 1990. C. de Concini, V. G. Kac, and C. Procesi, The quantum coadjoint action, preprint, 1991.
  • Pierre Dazord and D. Sondaz, Groupes de Poisson affines, Symplectic geometry, groupoids, and integrable systems (Berkeley, CA, 1989) Math. Sci. Res. Inst. Publ., vol. 20, Springer, New York, 1991, pp. 99–128 (French). MR 1104921, DOI 10.1007/978-1-4613-9719-9_{6}
  • V. G. Drinfel′d, Hamiltonian structures on Lie groups, Lie bialgebras and the geometric meaning of classical Yang-Baxter equations, Dokl. Akad. Nauk SSSR 268 (1983), no. 2, 285–287 (Russian). MR 688240
  • —, Quantum groups, Internat. Congr. Math. (Berkeley, 1986), Vol. 1, Amer. Math. Soc., Providence, RI, 1987, pp. 789-820.
  • J. J. Duistermaat, Convexity and tightness for restrictions of Hamiltonian functions to fixed point sets of an antisymplectic involution, Trans. Amer. Math. Soc. 275 (1983), no. 1, 417–429. MR 678361, DOI 10.1090/S0002-9947-1983-0678361-2
  • J. J. Duistermaat, On the similarity between the Iwasawa projection and the diagonal part, Mém. Soc. Math. France (N.S.) 15 (1984), 129–138. Harmonic analysis on Lie groups and symmetric spaces (Kleebach, 1983). MR 789082
  • V. L. Ginzburg, private communication, 1990.
  • V. Guillemin and S. Sternberg, Convexity properties of the moment mapping, Invent. Math. 67 (1982), no. 3, 491–513. MR 664117, DOI 10.1007/BF01398933
  • Sigurdur Helgason, Differential geometry, Lie groups, and symmetric spaces, Pure and Applied Mathematics, vol. 80, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1978. MR 514561
  • Alfred Horn, Doubly stochastic matrices and the diagonal of a rotation matrix, Amer. J. Math. 76 (1954), 620–630. MR 63336, DOI 10.2307/2372705
  • Y. Kosmann-Schwarzbach and F. Magri, Poisson-Lie groups and complete integrability. I. Drinfel′d bialgebras, dual extensions and their canonical representations, Ann. Inst. H. Poincaré Phys. Théor. 49 (1988), no. 4, 433–460 (English, with French summary). MR 988946
  • Bertram Kostant, On convexity, the Weyl group and the Iwasawa decomposition, Ann. Sci. École Norm. Sup. (4) 6 (1973), 413–455 (1974). MR 364552
  • Jean-Louis Koszul, Crochet de Schouten-Nijenhuis et cohomologie, Astérisque Numéro Hors Série (1985), 257–271 (French). The mathematical heritage of Élie Cartan (Lyon, 1984). MR 837203
  • Jiang-Hua Lu and Alan Weinstein, Poisson Lie groups, dressing transformations, and Bruhat decompositions, J. Differential Geom. 31 (1990), no. 2, 501–526. MR 1037412
  • Jiang-Hua Lu, Momentum mappings and reduction of Poisson actions, Symplectic geometry, groupoids, and integrable systems (Berkeley, CA, 1989) Math. Sci. Res. Inst. Publ., vol. 20, Springer, New York, 1991, pp. 209–226. MR 1104930, DOI 10.1007/978-1-4613-9719-9_{1}5
  • —, Multiplicative and affine Poisson structures on Lie groups, Ph.D. Thesis, University of California, Berkeley, 1990. N. Y. Reshetikhin, Poisson structures for quantum groups at roots of 1 , preprint, Harvard Univ., 1990. I. Schur, Über eine Klasse von Mittelbildungen mit Anwendungen auf der Determinanten Theorie, Sitzungsberichte der Berliner Mathematischen Gesellschaft 22 (1923), 9-20.
  • Michael A. Semenov-Tian-Shansky, Dressing transformations and Poisson group actions, Publ. Res. Inst. Math. Sci. 21 (1985), no. 6, 1237–1260. MR 842417, DOI 10.2977/prims/1195178514
  • Alan Weinstein, The local structure of Poisson manifolds, J. Differential Geom. 18 (1983), no. 3, 523–557. MR 723816
  • S. L. Woronowicz, Compact matrix pseudogroups, Comm. Math. Phys. 111 (1987), no. 4, 613–665. MR 901157
  • P. Xu, private communication, 1990.
Similar Articles
  • Retrieve articles in Journal of the American Mathematical Society with MSC: 58F05
  • Retrieve articles in all journals with MSC: 58F05
Additional Information
  • © Copyright 1991 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 4 (1991), 349-363
  • MSC: Primary 58F05
  • DOI: https://doi.org/10.1090/S0894-0347-1991-1086967-2
  • MathSciNet review: 1086967