no. 1
The irreducible unitary GL (n-1,ℝ)-spherical representations of SL (n,ℝ)
Compositio Mathematica, Tome 73 (1990) no. 1, pp. 1-30. 
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     title = {The irreducible unitary $\mathrm {GL} (n-1,\mathbb {R})$-spherical representations of $\mathrm {SL} (n, \mathbb {R})$},
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     pages = {1--30},
     publisher = {Kluwer Academic Publishers},
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     zbl = {0723.22018},
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Van Dijk, G.; Poel, M. The irreducible unitary $\mathrm {GL} (n-1,\mathbb {R})$-spherical representations of $\mathrm {SL} (n, \mathbb {R})$. Compositio Mathematica, Tome 73 (1990) no. 1, pp. 1-30. http://archive.numdam.org/item/CM_1990__73_1_1_0/

[Ba] J. Bang-Jensen: The Multiplicities of Certain K-types in Irreducible Spherical Representations of Semisimple Lie Groups. Thesis Massachusetts Institute of Technology, 1987.

[B-G] J.N. Bernstein and S.I. Gelfand: Tensor products of finite and infinite dimensional representations of semisimple Lie algebras. Comp. Math. 41 (1980), p. 245-285. | Numdam | MR | Zbl

[D-P] G Van Dijk & M. Poel: The Plancherel formula for the pseudo-Riemannian space SL(n, R)/GL(n-1, R). Comp. Math. 58 (1986) p. 371-397. | Numdam | MR | Zbl

[D] J. Dixmier: Enveloping Algebras. North-Holland Publishing Company, Amsterdam/ New York/Oxford, 1977. | MR | Zbl

[Fa] J. Faraut: Distributions sphériques sur les espaces hyperboliques. J. Math. Pures et Appl. 58 (1979), p. 369-444. | MR | Zbl

[F-K] M. Flensted-Jensen & T.H. Koornwinder: Positive definite spherical functions on a non-compact rank one symmetric space. In: Lect. Notes in Math. 739, Springer Verlag Berlin etc., 1979, p. 249-282. | MR | Zbl

[H] S. Helgason: A Duality for Symmetric Spaces with Applications to Group Representations I. Adv. Math. 5 (1970), p. 1-154. | MR | Zbl

[Kn] A.W. Knapp: Representation Theory of Semisimple Groups. An Overview Based on Examples. Princeton University Press, Princeton N.J., 1986. | MR | Zbl

[Ko] B. Kostant: On the existence and irreducibility of certain series of representations. In: I.M. Gelfand (ed.) Lie groups and their representations, Halsted Press, New-York, 1975, p. 231-329.(See also Bull. A.M.S. 75 (1969), p. 627-642.) | MR | Zbl

[MKo] M.T. Kosters: Spherical distributions on rank one symmetric spaces. Thesis University of Leiden, 1983.

[MKo-D] M.T. Kosters & G. Van Dijk: Spherical Distributions on the Pseudo-Riemannian space SL(n, R)/GL(n - 1, R). J. Funct. Anal. 68 (1986), p. 168-213. | MR | Zbl

[WKo] W.A. Kosters: Eigenspaces of the Laplace-Beltrami operator on SL(n, R)/S(GL(1) x GL(n - 1)), I and II. Ind. Math. 47 (1985), p. 99-145. | MR | Zbl

[M] V.F. Molčanov: The Plancherel formula for the pseudo-Riemannian space SL(3, R)/ GL(2, R). Sibirsk Math. J. 23 (1982), p. 142-151. | MR | Zbl

[P] M. Poel: Harmonic Analysis on SL(n, R)/GL(n - 1, R). Thesis University of Utrecht, 1986.

[T] E.G.F. Thomas: The theorem of Bochner-Schwartz-Godement for generalized Gelfand pairs. In: K.D. Bierstedt and B. Fuchsteiner (eds.), Functional Analysis: Surveys and recent results III, Elseviers Science Publishers B.V. (North Holland) (1984). | MR | Zbl

[Va] V.S. Varadarajan: Harmonic Analysis on Real Reductive Groups. Lecture Notes in Mathematics, No. 576, Springer-Verlag, Berlin/ Heidelberg/New York, 1977. | MR | Zbl

[Vo1] D.A. Vogan: Representations of Real Reductive Lie Groups. Birkhäuser, Boston/ Basel/ Stuttgart, 1981. | MR | Zbl

[Vo2] D.A. Vogan: The unitary dual of GL(n) over an archimedian field. Invent. Math. 83 (1985), p. 449-505. | MR | Zbl

[W] N.R. Wallach: Harmonic Analysis on Homogeneous Spaces. Dekker, New-York, 1977. | MR | Zbl

[Z] G. Zuckerman: Tensor products of finite and infinite dimensional representations of semisimple Lie groups. Ann. Math. 106 (1977), p. 295-308. | MR | Zbl