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Complex generalized Gelfand pairs

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In this article we show that the pairs (SO(n, C), SO(n-1, C)) are generalized Gelfand pairs for n≥

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7-12

References

1. S. Aparicio. Invariant Hilbert spaces of the oscillator representation. Thesis Univ. Leiden, 2005. 2. Y. Benoist. Multiplicité un pour les espaces symétriques exponentiels. Mém. Soc. Math. Fr., Nouv. Sér., 1984, torn 15, 1-37. 3. G. van Dijk. On generalized Gelfand pairs. Proc. Japan Acad. Ser. A, Math. Sci., 1984, vol. 60, No. 1, 30-34. 4. G. van Dijk. On a class of generalized Gelfand pairs. Math. Z., 1986, Bd. 193, No.4, 581-593. 5. G. van Dijk, M. Poel. The Plancherel formula for the pseudo-Riemannian space SL(n,R)/GL(n-1,R). Compositio Math., 1986, vol. 58, No. 3, 371-397. 6. M. W. Hirsch. Differential Topology. Grad. Texts in Math., vol. 33, Springer-Verlag, New York, 1976. 7. M. T. Kosters. Spherical distributions on rank one symmetric spaces. Thesis Univ. Leiden, 1983. 8. W. A. Kosters. Harmonic analysis on symmetric spaces. Thesis Univ. Leiden, 1985. 9. S. Rallis, G. Schiffmann. Distributions invariantes par le groupe orthogonal. In: Analyse harmonique sur les groupes de Lie (Sém. Nancy-Strasbourg, 1973-75). Lecture Notes in Math., vol. 497, 494-642, Springer, Berlin, 1975. 10. E. G. F. Thomas. The theorem of Bochner-Schwartz-Godement for generalized Gelfand pairs. In: Functional anlysis; surveys and recent results, III (Paderborn, 1983). North-Holland Math. Stud., vol. 90, 291-304, North-Holland, Amsterdam, 1984.

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