## Holomorphic discrete series for the real symplectic group.(English)Zbl 0236.22013

### MSC:

 2.2e+46 Representations of Lie and linear algebraic groups over real fields: analytic methods
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### References:

 [1] Bochner, S.: Bessel functions and modular relations of higher type and hyperbolic differential equations. Com. Sem. Math. de l’Univ. de Lund 12-20 (1952). · Zbl 0047.35002 [2] Boerner, H.: Representations of groups. Amsterdam: North-Holland Publishing Co. 1963. · Zbl 0112.26301 [3] Gelbart, S.: Stiefel manifold harmonics and generalized Hankel transforms. Bulletin of the A.M.S.78, 451-455 (1972) see also ?A theory of Stiefel harmonics?, to appear. · Zbl 0235.43012 [4] Godement, R.: Seminaire Cartan: Functions automorphes, Institut Poincaré. Paris: Secrétariat mathématique 1958. [5] Gross, K., Kunze, R.: Fourier Bessel transforms and holomorphic discrete series. In: Proceedings of the Maryland Conference on Harmonic Analysis. Notes in Mathematics.266. Berlin-Heidelberg-New York: Springer 1972. · Zbl 0242.22015 [6] Harish-Chandra, .: Representations of semi-simple Lie groups, IV, V, VI. Amer. J. of Math. 77-78 (1955-1956). [7] Knapp, A. W., Okamoto, K.: Limits of holomorphic discrete series. J. of Functional Analysis9, 375-409 (1972). · Zbl 0226.22010 [8] Saito, M.: Representations unitaires des groupes symplectiques. C. R. Acad. Sc. Paris267, 500-503 (1968). · Zbl 0164.34103 [9] Shalika, J.: Representations of the two-by-two unimodular group over local fields. Seminar on Lie group representations, mimeographed notes, Princeton 1966. [10] Tanaka, S.: On irreducible unitary representations of some special linear groups of the second order, I. Osaka J. Math.3, 217-227 (1966). · Zbl 0145.38805 [11] Weil, A.: Sur certains groupes d’opérateurs unitaires. Acta. Math.111, 143-211 (1964). · Zbl 0203.03305
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