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On singular holomorphic representations. (English) Zbl 0466.22016


MSC:

22E46 Semisimple Lie groups and their representations

Citations:

Zbl 0375.22009
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References:

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[2] Gross, K., Holman, W.: Matrix-valued special functions and representation theory of the conformal group, I: The generalized gamma function. Preprint 1977 · Zbl 0427.22008
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[4] Jakobsen, H.P., Vergne, M.: Wave and Dirac operators and representations of the conformal group. J. Functional Analysis24, 52-106 (1977) · Zbl 0361.22012 · doi:10.1016/0022-1236(77)90005-2
[5] Jakobsen, H.P.: Tensor products, reproducing kernels, and power series, J. Functional Analysis31, 293-305 (1979) · Zbl 0403.22011 · doi:10.1016/0022-1236(79)90004-1
[6] Jakobsen, H.P., Vergne, M.: Restrictions and expansions of holomorphic representations, J. Functional Analysis34, 29-53 (1979) · Zbl 0433.22011 · doi:10.1016/0022-1236(79)90023-5
[7] James, G.D.: The Representation Theory of the Symmetric Groups, Lecture Notes in Math. 682, Berlin-Heidelberg-New York: Springer Verlag 1978 · Zbl 0393.20009
[8] Kashiwara, M., Vergne, M.: On the Segal-Shale-Weil representation and harmonic polynomials, Invent. Math.44, 1-47 (1978) · Zbl 0375.22009 · doi:10.1007/BF01389900
[9] Mack, G.: All unitary ray representations of the conformal groupSU(2,2) with positive energy, Comm. Math. Phys.55, 1-28 (1977) · Zbl 0352.22012 · doi:10.1007/BF01613145
[10] Parthasarathy, R.: Criteria for the unitarizability of some highest weight modules. Preprint 1978 · Zbl 0434.22011
[11] Rossi, H., Vergne, M.: Analytic continuation of the holomorphic discrete series of a semi-simple Lie group, Acta Math.136, 1-59 (1976) · Zbl 0356.32020 · doi:10.1007/BF02392042
[12] Schmid, W.: Die Randwerte holomorpher Funktionen auf Hermitesch symmetrischen Räumen, Invent. Math.9, 61-80 (1969) · Zbl 0219.32013 · doi:10.1007/BF01389889
[13] Schur, I.: Dissertation, Berlin, 1901
[14] Wallach, N.: The analytic continuation of the discrete series I, II, to appear in Trans. Amer. Math. Soc.
[15] Williams, F.: Unitarizable highest weight modules of the conformal group. Preprint 1979
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