Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On the Kostant convexity theorem

Author: François Ziegler
Journal: Proc. Amer. Math. Soc. 115 (1992), 1111-1113
MSC: Primary 22E60; Secondary 22E15, 58F06
MathSciNet review: 1111441
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A quick proof that the coadjoint orbits of a compact connected Lie group project onto convex polytopes in the dual of a Cartan subalgebra.

References [Enhancements On Off] (What's this?)

  • [1] J. F. Adams, Lectures on Lie groups, Benjamin, New York and Amsterdam, 1969. MR 0252560 (40:5780)
  • [2] M. F. Atiyah, Convexity and commuting hamiltonians, Bull. London Math. Soc. 14 (1982), 1-15. MR 642416 (83e:53037)
  • [3] M. Audin, The topology of torus actions on symplectic manifolds, Prog. Math., vol. 93, Birkhäuser, Basel, 1991. MR 1106194 (92m:57046)
  • [4] R. Bott, The geometry and representation theory of compact Lie groups, Representation Theory of Lie Groups (M. F. Atiyah, ed.), Cambridge Univ. Press, 1979, pp. 65-90. MR 568880 (81j:22001)
  • [5] V. Guillemin and S. Sternberg, Convexity properties of the moment mapping, Invent. Math. 67 (1982), 491-513. MR 664117 (83m:58037)
  • [6] -, Geometric quantization and multiplicities of group representations, Invent. Math. 67 (1982), 515-538. MR 664118 (83m:58040)
  • [7] G. J. Heckman, Projections of orbits and asymptotic behaviour of multiplicities for compact Lie groups, Thesis, Leiden, 1980.
  • [8] -, Projections of orbits and asymptotic behavior of multiplicities for compact connected Lie groups, Invent. Math. 67 (1982), 333-356. MR 665160 (84d:22019)
  • [9] B. Kostant, On convexity, the Weyl group and the Iwasawa decomposition, Ann. Sci. École Norm. Sup. (4) 6 (1973), 413-455. MR 0364552 (51:806)
  • [10] J. P. Serre, Représentations linéaires et espaces homogènes kählériens des groupes de Lie compacts (d'après A. Borel & A. Weil), Séminaire Bourbaki 100 (1954).
  • [11] J. M. Souriau, Structure des systèmes dynamiques, Dunod, Paris, 1969. MR 0260238 (41:4866)
  • [12] J. Tits, Sur certaines classes d'espaces homogènes de groupes de Lie, Mém. Acad. Roy. Belg. Cl. Sci. 29 (1955). MR 0076286 (17:874f)
  • [13] V. G. Kac and D. H. Peterson, Unitary structure in representations of infinite-dimensional groups and a convexity theorem, Invent. Math. 76 (1984), 1-14. MR 739620 (86g:17013)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 22E60, 22E15, 58F06

Retrieve articles in all journals with MSC: 22E60, 22E15, 58F06

Additional Information

Article copyright: © Copyright 1992 American Mathematical Society

American Mathematical Society