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Bessel functions and representation theory. II: Holomorphic discrete series and metaplectic representations. (English) Zbl 0361.22007


MSC:

22E45 Representations of Lie and linear algebraic groups over real fields: analytic methods
33C80 Connections of hypergeometric functions with groups and algebras, and related topics
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[1] Gross, K. I.; Kunze, R. A., Bessel functions and representation theory, I, J. Functional Analysis, 22, 73-105 (1976) · Zbl 0322.43014
[2] Gross, K. I.; Kunze, R. A., Fourier Bessel transforms and holomorphic discrete series, (Conference on Harmonic Analysis. Conference on Harmonic Analysis, Springer Lecture Notes, Vol. 266 (1972)) · Zbl 0268.43010
[3] Godement, R., Fonctions automorphes, (Seminaire Cartan (1957-1958), University of Paris) · Zbl 0217.43303
[4] Zelobenko, D. P., Compact Lie Groups and Their Representations (1973), American Mathematical Society: American Mathematical Society Providence, R.I · Zbl 0272.22006
[5] Wallach, N., Induced representations of Lie algebras, and a theorem of Borel-Weil, Trans. Amer. Math. Soc., 136, 181-187 (1969) · Zbl 0294.17005
[6] K. I. Gross and R. A. Kunze; K. I. Gross and R. A. Kunze · Zbl 0567.22007
[7] Rossi, H.; Vergne, M., Representations of certain solvable Lie groups on Hilbert spaces of holomorphic functions and the application to the holomorphic discrete series of a semisimple Lie group, J. Functional Analysis, 13, 324-389 (1973) · Zbl 0279.32019
[8] Hua, L. K., Harmonic Analysis of Functions of Several Complex Variables in the Classical Domains (1963), American Mathematical Society: American Mathematical Society Providence, R.I · Zbl 0112.07402
[9] Kunze, R. A., Positive definite operator-valued kernels and unitary representations, (Proceedings of the Conference on Functional Analysis at Irvine. Proceedings of the Conference on Functional Analysis at Irvine, California (1966), Thompson Book Company) · Zbl 0226.43011
[10] Kunze, R. A.; Stein, E. M., Uniformly bounded representations III, Amer. J. Math., 89, 385-442 (1967) · Zbl 0195.14202
[11] Shale, D., Linear symmetries of free Boson fields, Trans. Amer. Math. Soc., 103, 149-169 (1962) · Zbl 0171.46901
[12] Segal, I. E., Transforms for operators and symplectic automorphisms over a locally compact abelian group, Math. Scand., 13, 31-43 (1963) · Zbl 0208.39002
[13] Weil, A., Sur certaines groupes d’opérateurs unitaires, Acta Math., 111, 143-211 (1964) · Zbl 0203.03305
[14] Gross, K. I., The dual of a parabolic subgroup and a degenerate principal series of Sp(n \(C\), Amer. J. Math., 93, 398-428 (1971) · Zbl 0229.22025
[15] Gross, K. I.; Kunze, R. A., Generalized Bessel transforms and unitary representations, (Harmonic Analysis on Homogeneous Spaces. Harmonic Analysis on Homogeneous Spaces, American Mathematical Society Symposium, XXVI (1973)), 347-350 · Zbl 0289.22014
[16] Gelbart, S., Holomorphic discrete series for the real symplectic groups, Invent. Math., 19, 49-58 (1973) · Zbl 0236.22013
[17] H. Rossi and M. Vergne; H. Rossi and M. Vergne · Zbl 0356.32020
[18] N. WallachTrans. Amer. Math. Soc.; N. WallachTrans. Amer. Math. Soc. · Zbl 0419.22018
[19] Harish-Chandra, Representations of semisimple Lie groups V, Amer. J. Math., 78, 1-41 (1956) · Zbl 0070.11602
[20] Knapp, A.; Okamoto, K., Limits of holomorphic discrete series, J. Functional Analysis, 9, 375-409 (1972) · Zbl 0226.22010
[21] Gross, K. I.; Holmar, W. J.; Kunze, R. A., The generalized gamma function, new hardy spaces, and representations of holomorphic type for the conformal group, Bulletin Amer. Math. Soc., 83 (1977) · Zbl 0349.22007
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