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References
Atiyah, M. F., Bott, R., Shapiro, A.: Clifford modules. Topology3, 3–38 (1964)
Bott, R.: Homogeneous vector bundles. Ann. of Math.66, 203–243 (1957)
Chevalley, C.: The algebraic theory of spinors. New York: Columbia University Press 1954
Gangolli, R.: Spectra of discrete subgroups. Proc of Summer Inst. of A.M.S. at Williamstown, 1972
Gunning, R. C., Rossi, H.: Analytic functions of several complex variables Englewood Cliffs: Prentice-Hall 1965
Harish-Chandra: Representations of semisimple Lie groups: IV, V, VI. Amer. J. Math.77, 743–777 (1955);78, 1–41 and 564–628 (1956)
Harish-Chandra: Discrete series for semisimple Lie groups: II. Acta Math.116, 1–111 (1966)
Hotta, R.: Elliptic complexes on certain homogeneous spaces. Osaka J. Math.7, 117–160 (1970)
Hotta, R.: On realization of the discrete series for semisimple Lie groups. J. of Math. Soc. Japan23, 384–407 (1971)
Hotta, R., Parthasarathy, R.: A geometric meaning of the multiplicity of integrable discrete classes inL 2 (Γ-G). To appear in Osaka J. Math.
iwahori, N.: Lie gun ron: II (in Japanese) Tokyo: Iwanami 1957
Kostant, B.: Lie algebra cohomology and the generalized Borel-Weil therem. Ann. of Math.74, 329–387 (1961)
Langlands, R. P.: The dimension of spaces of automorphic forms. Amer. J. Math.85, 99–125 (1963)
Langlands, R. P.: Dimension of spaces of automorphic forms. Proc. of Symposia in Pure Math., A.M.S.IX, 253–257 (1966)
Matsushima, Y., Murakami, S.: On certain cohomology groups attached to hermitian symmetric spaces: (II). Osaka J. Math.5, 223–241 (1968)
Narasimhan, M. S., Okamoto, K.: An analogue of the Borel-Weil-Bott theorem for hermitian symmetric pairs of non-compact type. Ann. of Math.91, 486–511 (1970)
Palais, R. S.,et al., Seminar on the Atiyah-Singer index theorem. Ann. of Math. Studies57, Princeton University Press, 1965
Parthasarathy, R.: Dirac operator and the discrete series. Ann. of Math.96, 1–30 (1972)
Parthasarathy, R.: A note on the vanishing of certain “L 2-cohomologies”. J. of Math. Soc. Japan23, 676–691 (1971)
Schmid, W.: Homogeneous complex manifolds and representations of semisimple Lie groups. Thesis at Univ. of California-Berkeley, 1967. Proc. Nat. Acad. Sci. U.S.A.59, 56–59 (1968)
Schmid, W.: On a conjecture of Langlands. Ann. of Math.93, 1–42 (1971)
Schmid, W.: On the realization of the discrete series of a semisimple Lie group. Rice Univ. Studies56, 99–108 (1970)
Trombi, P. C., Varadarajan, V. S.: Asymptotic behaviour of eigenfunctions on a semisimple Lie group: the discrete spectrum. Acta Math.129, 237–280 (1972)
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Research partially supported by NSF grant GP-36418 X.
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Hotta, R., Parthasarathy, R. Multiplicity formulae for discrete series. Invent Math 26, 133–178 (1974). https://doi.org/10.1007/BF01435692
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DOI: https://doi.org/10.1007/BF01435692