zbMATH — the first resource for mathematics

Convexity properties of the moment mapping. (English) Zbl 0503.58017

53D50 Geometric quantization
37J15 Symmetries, invariants, invariant manifolds, momentum maps, reduction (MSC2010)
22F05 General theory of group and pseudogroup actions
53D20 Momentum maps; symplectic reduction
Full Text: DOI EuDML
[1] Abraham, R., Marsden, J.: Foundations of mechanics. Reading, MA: Benjamin 1978 · Zbl 0393.70001
[2] Arms, J., Marsden, J., Moncrief, V.: Symmetries and bifurcations of the momentum mapping. Commun. Math. Phys.78, 455-478 (1981) · Zbl 0486.58008 · doi:10.1007/BF02046759
[3] Atiyah, M.: Convexity and commuting Hamiltonians. (preprint) · Zbl 0482.58013
[4] Bott, R.: Non-degenerate critical manifolds. Ann. of Math.60, 248-261 (1954) · Zbl 0058.09101 · doi:10.2307/1969631
[5] Heckman, G.: Projections of orbits and asymptotic behavior of multiplicities for compact Lie groups. (preprint) · Zbl 0497.22006
[6] Humphreys, J.E.: Introduction to Lie algebras and representation theory. Berlin-Heidelberg-New York: Springer 1972 · Zbl 0254.17004
[7] Kostant, B.: On convexity, the Weyl group and the Iwasawa decomposition. Ann. Sci. Ec. Norm. Sup.6, 413-455 (1973) · Zbl 0293.22019
[8] Kostant, B.: Quantization and unitary representations. In: Lecture Notes in Mathematics, Vol. 170. Berlin-Heidelberg-New York: Springer 1970 · Zbl 0223.53028
[9] Marsden, J., Weinstein, A.: Reduction of symplectic manifolds with symmetry. Rep. Math. Phys.5, 121-130 (1974) · Zbl 0327.58005 · doi:10.1016/0034-4877(74)90021-4
[10] Montgomery, D., Samelson, H., Zippin, L.: Singular points of compact transformation groups. Ann. of Math. (2)63, 1-9 (1956) · Zbl 0074.25905 · doi:10.2307/1969986
[11] Mostow, G.D.: On a conjecture of Montgomery. Ann. of Math. (2)65, 513-516 (1957) · Zbl 0078.16302 · doi:10.2307/1970061
[12] Sternberg, S.: Lectures on differential geometry. Englewood Cliffs, NJ: Prentice-Hall 1964 · Zbl 0129.13102
[13] Yang, C.-T.: On a problem of Montgomery, Proc. Am. Math. Soc.8, 255-275 (1957) · Zbl 0078.16303 · doi:10.1090/S0002-9939-1957-0087040-4
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.