Inventiones mathematicae

, Volume 67, Issue 3, pp 515–538 | Cite as

Geometric quantization and multiplicities of group representations

  • V. Guillemin
  • S. Sternberg
Article

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Atiyah, M.F.: Convexity and commuting Hamiltonians. Bull. Lon. Math. Soc. 14 (1982) 1–15Google Scholar
  2. 2.
    Boutet de Monvel, L., Sjöstrand, J.: Sur la singularité des noyaux de Bergmann et de Szegö. Asterisque34–35, 123–164 (1976)Google Scholar
  3. 3.
    Boutet de Monvel, L., Guillemin, V.: The spectral theory of toeplitz operators. Annals of Math. Studies Vol. 99. Princeton, NJ: Princeton University Press 1981Google Scholar
  4. 4.
    Guillemin, V., Sternberg, S.: Some problems in integral geometry and some related problems in micro-local analysis. Am. J. Math.101, 915–955 (1979)Google Scholar
  5. 5.
    Guillemin, V., Sternberg, S.: Convexity properties of the moment mapping. Invent. Math. in press (1982)Google Scholar
  6. 6.
    Heckman, G.: Projections of orbits and asymptotic behavior of multiplicities for compact Lie groups. Thesis, Leiden (1980)Google Scholar
  7. 7.
    Hörmander, L.: Fourier integral operators I. Acta Math.127, 79–183 (1972)Google Scholar
  8. 8.
    Kempf, G., Ness, L.: The length of vectors in representation space. Lect. notes in Math. 732 (1979). Springer-VerlagGoogle Scholar
  9. 9.
    Kobayashi, S.: Geometry of bounded domains. Trans. Amer. Math. Soc.92, 267–290 (1959)Google Scholar
  10. 10.
    Kostant, B.: Orbits, symplectic structures, and representation theory. Proc. US-Japan Seminar in Differential Geometry, Kyoto, (1965), Nippon Hyoronsha, Tokyo, 1966Google Scholar
  11. 11.
    Kostant, B.: Quantization and unitary representations. In: Modern analysis and applications. Lecture Notes in Math., Vol. 170, pp. 87–207. Berlin-Heidelberg-New York: Springer 1970Google Scholar
  12. 12.
    Marsden, J., Weinstein, A.: Reduction of symplectic manifolds with symmetry. Reports on Math. Phys.5, 121–130 (1974)Google Scholar
  13. 13.
    Melin, A., Sjöstrand, J.: Fourier integral operators with complex phase functions. In: Fourier integral operators and partial differential equations. Lecture Notes, vol. 459. pp. 120–223. Berlin-Heidelberg-New York: Springer 1975Google Scholar
  14. 14.
    Mumford, D.: Geometric invariant theory. Ergebnisse der Math., Vol. 34. Berlin-Heidelberg-New York: Springer 1965Google Scholar
  15. 15.
    Simms, D., Woodhouse, N.: Lectures on geometric quantization. Lectures Notes in Physics, Vol. 53. Berlin-Heidelberg-New York: Springer 1976Google Scholar
  16. 16.
    Weinstein, A.: Lectures on symplectic manifolds, AMS, Regional Conference in Mathematics Series, Vol. 29, AMS, Providence, R.I. 1976Google Scholar
  17. 17.
    Weinstein, A.: Symplectic geometry. Bull. Am. Math. Soc.5, 1–13 (1981)Google Scholar
  18. 18.
    Atiyah, M., Singer, I.M.: The index of elliptic operators, III. Ann. of Math.87, 546–604 (1968)Google Scholar
  19. 19.
    Kawasaki, T.: The Riemann-Roch theorem for complexV-manifolds. Osaka Journal of Math.16, 151–159 (1979)Google Scholar
  20. 20.
    Satake, I.: On a generalization of the notion of manifold. Proc. Nat. Acad. Sci. USA42, 359–363 (1956)Google Scholar
  21. 21.
    Weinstein, A.: SymplecticV-manifolds, periodic orbits of Hamiltonian systems and the volume of certain Riemann manifolds. Comm. Pure and App. Math.30, 265–271 (1977)Google Scholar

Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • V. Guillemin
    • 1
  • S. Sternberg
    • 1
  1. 1.Departments of MathematicsMass. Inst. of Tech. and Harvard UniversityCambridgeUSA

Personalised recommendations