Journal of Differential Geometry

Multiplicity-free spaces

Victor Guillemin and Shlomo Sternberg

Full-text: Open access

Article information

Source
J. Differential Geom., Volume 19, Number 1 (1984), 31-56.

Dates
First available in Project Euclid: 26 June 2008

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1214438422

Digital Object Identifier
doi:10.4310/jdg/1214438422

Mathematical Reviews number (MathSciNet)
MR739781

Zentralblatt MATH identifier
0548.58017

Subjects
Primary: 58F06
Secondary: 22E45: Representations of Lie and linear algebraic groups over real fields: analytic methods {For the purely algebraic theory, see 20G05}

Citation

Guillemin, Victor; Sternberg, Shlomo. Multiplicity-free spaces. J. Differential Geom. 19 (1984), no. 1, 31--56. doi:10.4310/jdg/1214438422. https://projecteuclid.org/euclid.jdg/1214438422


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References

  • [1] J. Arms, J. Marsden and V. Moncrief, Symmetries and bifurcations of the momentum mapping, Comm. Math. Phys. 78 (1981) 455-478.
  • [2] M. Atiyah, Convexity and commuting Hamiltonians, Bull. London Math. Soc. 14 (1982) 1-15.
  • [3] M. Gotay and J. Nester, Presymplectic manifolds and the Dirac-Bergmann theory of constraints, J. Math. Phys. 19 (1978) 2388-2399.
  • [4] V. Guillemin, M. Kashiwara and T. Kawai, Seminar on micro-local analysis, Annals of Math. Studies No. 93, Princeton University Press, Princeton, NJ, 1979.
  • [5] V. Guillemin and S. Sternberg, On the equations of motion of a classical particle ina Yang-Mills field and the principal of general covariance, Hadronic J. 1 (1978) 1-32.
  • [6] V. Guillemin and S. Sternberg, The moment map and collective motion, Ann. Physics. 127 (1980) 220-253.
  • [7] V. Guillemin and S. Sternberg, Moments and reductions, Diff. Geom. Meth. in Math. Phys. Proc. (Clausthal, 1980), Lecture Notes in Math. Vol. 905, Springer, Berlin, 1982, 52-65.
  • [8] V. Guillemin and S. Sternberg, The Frobenius reciprocity theorem from the symplectic point of view, Diff. Geom. Methods in Math. Phys. Proc., Clausthal, 1981.
  • [9] V. Guillemin and S. Sternberg, Convexity properties of the moment map, Invent. Math. 67 (1982) 491-513.
  • [10] V. Guillemin and S. Sternberg, Geometric quantization and multiplicities of group representations, Invent. Math. 67 (1982) 515-538.
  • [11] V. Guillemin and S. Sternberg, Homogeneous quantization and multiplicities of group representations, J. Funct. Anal. 47 (1982) 344-380.
  • [12] V. Guillemin and S. Sternberg, On collective complete integrability according to the method of Thimm, Ergodic Theory Dynamical Systems, to appear.
  • [13] S. Helgason, Differential geometry and symmetric spaces, Academic Press, New York, 1962.
  • [14] J. Humphreys, Introduction to Lie algebras and representation theory, Springer, New York, 1972.
  • [15] D. Kazhdan, B. Kostant and S. Stemberg, Hamiltonian group actions and dynamical systems of Calogero type, Comm. Pure Appl. Math. 31 (1978) 481-507.
  • [16] F. Kirwan, The cohomology of quotient spaces in algebraic geometry, Thesis, Oxford, 1982.
  • [17] B. Kostant, Proceedings of the Clalusthal Conference in Mathematical Physics (July 1981), to appear.
  • [18] M. Kramer, Spharische Untergruppen in kompacten zusammenhangenden Lie Gruppen, Compositio Math. 38 (1979) 129-153.
  • [19] J. Marsden and A. Weinstein, Reduction of symplectic manifolds with symmetry, J. Math. Phys. 5 (1974) 121-130.
  • [20] A. S. Mishchenko and A. T. Fomenko, A generalized Liouville method for the integration of Hamiltonian systems, Funktsional Anal. i Prilozen 12 (1978) 46-56.
  • [21] L. Ness, A stratification of the null cone via the moment map, Amer. J. Math., to appear.
  • [22] E. A. Planchart, Analogies in symplectic geometry of some results of Carton in representation theory, Thesis, Berkeley, 1982.
  • [23] S. Sternberg, Minimal coupling and the symplectic mechanics of a classical particle in the presence of a Yang-Mills field, Proc. Nat. Acad. Sci. U.S.A. 74 (1977) 5253-5254.
  • [24] S. Sternberg and T. Ungar, Classical and prequantized mechanics without Lagrangians or Hamiltonians, Hadronic J. 1 (1978) 33-45.
  • [25] A. Weinstein, Lectures on symplectic manifolds, CBMS Regional Conference Series in Math. No. 29, Amer. Math. Soc, Providence, RI, 1977.
  • [26] A. Weinstein, A universal phase space for particles in Yang-Mills fields, Lett. Math. Phys. 2 (1977/78) 417-420.
  • [27] A. Weinstein, Fat bundles and symplectic manifolds, Advances in Math. 37 239-250.
  • [28] A. Weinstein, Symplectic geometry, Bull. Amer. Math. Soc. (N. S.) 5 (1981) 1-13.
  • [29] A. Weinstein, Neighborhood classification of isotropic embedding, J. Differential Geometry 16 (1981) 125-128.
  • [30] A. Weinstein, The local structure of Poisson manifolds, Berkeley, 1982 (preprint).