On the Kostant convexity theorem

On the Kostant convexity theorem
HTML articles powered by AMS MathViewer

Proc. Amer. Math. Soc. 115 (1992), 1111-1113

DOI: https://doi.org/10.1090/S0002-9939-1992-1111441-7

PDF | Request permission

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

J. Frank Adams, Lectures on Lie groups, W. A. Benjamin, Inc., New York-Amsterdam, 1969. MR 0252560
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
Michèle Audin, The topology of torus actions on symplectic manifolds, Progress in Mathematics, vol. 93, Birkhäuser Verlag, Basel, 1991. Translated from the French by the author. MR 1106194, DOI 10.1007/978-3-0348-7221-8
G. L. Luke (ed.), Representation theory of Lie groups, Cambridge University Press, Cambridge, 1979. MR 568880
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
V. Guillemin and S. Sternberg, Geometric quantization and multiplicities of group representations, Invent. Math. 67 (1982), no. 3, 515–538. MR 664118, DOI 10.1007/BF01398934

Projections of orbits and asymptotic behaviour of multiplicities for compact Lie groups

G. J. Heckman, Projections of orbits and asymptotic behavior of multiplicities for compact connected Lie groups, Invent. Math. 67 (1982), no. 2, 333–356. MR 665160, DOI 10.1007/BF01393821
Bertram Kostant, On convexity, the Weyl group and the Iwasawa decomposition, Ann. Sci. École Norm. Sup. (4) 6 (1973), 413–455 (1974). MR 364552

Représentations linéaires et espaces homogènes kählériens des groupes de Lie compacts (d’après A. Borel & A. Weil)

100

J.-M. Souriau, Structure des systèmes dynamiques, Dunod, Paris, 1970 (French). Maîtrises de mathématiques. MR 0260238
J. Tits, Sur certaines classes d’espaces homogènes de groupes de Lie, Acad. Roy. Belg. Cl. Sci. Mém. Coll. in 8$^\circ$ 29 (1955), no. 3, 268 (French). MR 76286
V. G. Kac and D. H. Peterson, Unitary structure in representations of infinite-dimensional groups and a convexity theorem, Invent. Math. 76 (1984), no. 1, 1–14. MR 739620, DOI 10.1007/BF01388487