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On the Segal-Shale-Weil representations and harmonic polynomials. (English) Zbl 0375.22009

22E45Analytic representations of Lie and linear algebraic groups over real fields
22E30Analysis on real and complex Lie groups
32M15Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (analytic spaces)
43A32Other transforms and operators of Fourier type
43A85Analysis on homogeneous spaces
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[2]Gelbart, S.: Harmonics on Stiefel manifolds and generalized Hankel transforms. B.A.M.S.78, 451-455 (1972) · Zbl 0235.43012 · doi:10.1090/S0002-9904-1972-12941-0
[3]Gelbart, S.: Holomorphic discrete series for the real symplectic group. Inventiones math.19, 49-58 (1973) · Zbl 0236.22013 · doi:10.1007/BF01418850
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[8]Jacobsen, H., Vergne, M.: Wave and Dirac operators and representations of the conformal group. To appear in J. Funct. Anal.
[9]Joseph, A.: The minimal orbit in a simple Lie algebra and its associated maximal Ideal. Annales Scientifiques de l’Ecole Normale Superieure9, 1-30 (1976)
[10]Levine, D.A.: Systems of singular integral operators on spheres. Trans. Am. Math. Soc.144, 493-522 (1969) · doi:10.1090/S0002-9947-1969-0412743-1
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[12]Rossi, H., Vergne, M.: Analytic continuation of the holomorphic discrete series of a semi-simple group. Acta Mathematica136, 1-59 (1976) · Zbl 0356.32020 · doi:10.1007/BF02392042
[13]Segal, E.: Foundations of the theory of dynamical systems of infinitely many degrees of freedom. Mat. fys. Medd. Danske Vid. Selsk,31 (12), 1-39 (1959)
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[17]Strichartz, R.S.: Bochner identities for Fourier transforms. Trans. A.M.S.228, 307-327 (1977) · doi:10.1090/S0002-9947-1977-0433147-6
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[19]Wallach, N.: Analytic continuation of the holomorphic discrete series II. To appear
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