Advertisement

Inventiones mathematicae

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

Geometric quantization and multiplicities of group representations

  • V. Guillemin
  • S. Sternberg
Article

Keywords

Group Representation Geometric Quantization 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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