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Atiyah, M.F.: Convexity and commuting Hamiltonians. Bull. Lon. Math. Soc. 14 (1982) 1–15
Boutet de Monvel, L., Sjöstrand, J.: Sur la singularité des noyaux de Bergmann et de Szegö. Asterisque34–35, 123–164 (1976)
Boutet de Monvel, L., Guillemin, V.: The spectral theory of toeplitz operators. Annals of Math. Studies Vol. 99. Princeton, NJ: Princeton University Press 1981
Guillemin, V., Sternberg, S.: Some problems in integral geometry and some related problems in micro-local analysis. Am. J. Math.101, 915–955 (1979)
Guillemin, V., Sternberg, S.: Convexity properties of the moment mapping. Invent. Math. in press (1982)
Heckman, G.: Projections of orbits and asymptotic behavior of multiplicities for compact Lie groups. Thesis, Leiden (1980)
Hörmander, L.: Fourier integral operators I. Acta Math.127, 79–183 (1972)
Kempf, G., Ness, L.: The length of vectors in representation space. Lect. notes in Math. 732 (1979). Springer-Verlag
Kobayashi, S.: Geometry of bounded domains. Trans. Amer. Math. Soc.92, 267–290 (1959)
Kostant, B.: Orbits, symplectic structures, and representation theory. Proc. US-Japan Seminar in Differential Geometry, Kyoto, (1965), Nippon Hyoronsha, Tokyo, 1966
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 1970
Marsden, J., Weinstein, A.: Reduction of symplectic manifolds with symmetry. Reports on Math. Phys.5, 121–130 (1974)
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 1975
Mumford, D.: Geometric invariant theory. Ergebnisse der Math., Vol. 34. Berlin-Heidelberg-New York: Springer 1965
Simms, D., Woodhouse, N.: Lectures on geometric quantization. Lectures Notes in Physics, Vol. 53. Berlin-Heidelberg-New York: Springer 1976
Weinstein, A.: Lectures on symplectic manifolds, AMS, Regional Conference in Mathematics Series, Vol. 29, AMS, Providence, R.I. 1976
Weinstein, A.: Symplectic geometry. Bull. Am. Math. Soc.5, 1–13 (1981)
Atiyah, M., Singer, I.M.: The index of elliptic operators, III. Ann. of Math.87, 546–604 (1968)
Kawasaki, T.: The Riemann-Roch theorem for complexV-manifolds. Osaka Journal of Math.16, 151–159 (1979)
Satake, I.: On a generalization of the notion of manifold. Proc. Nat. Acad. Sci. USA42, 359–363 (1956)
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)
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Guillemin, V., Sternberg, S. Geometric quantization and multiplicities of group representations. Invent Math 67, 515–538 (1982). https://doi.org/10.1007/BF01398934
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DOI: https://doi.org/10.1007/BF01398934