@article{CM_1990__73_1_1_0, author = {Van Dijk, G. and Poel, M.}, title = {The irreducible unitary $\mathrm {GL} (n-1,\mathbb {R})$-spherical representations of $\mathrm {SL} (n, \mathbb {R})$}, journal = {Compositio Mathematica}, pages = {1--30}, publisher = {Kluwer Academic Publishers}, volume = {73}, number = {1}, year = {1990}, zbl = {0723.22018}, mrnumber = {1042452}, language = {en}, url = {http://www.numdam.org/item/CM_1990__73_1_1_0/} }
TY - JOUR AU - Van Dijk, G. AU - Poel, M. TI - The irreducible unitary $\mathrm {GL} (n-1,\mathbb {R})$-spherical representations of $\mathrm {SL} (n, \mathbb {R})$ JO - Compositio Mathematica PY - 1990 SP - 1 EP - 30 VL - 73 IS - 1 PB - Kluwer Academic Publishers UR - http://www.numdam.org/item/CM_1990__73_1_1_0/ LA - en ID - CM_1990__73_1_1_0 ER -
%0 Journal Article %A Van Dijk, G. %A Poel, M. %T The irreducible unitary $\mathrm {GL} (n-1,\mathbb {R})$-spherical representations of $\mathrm {SL} (n, \mathbb {R})$ %J Compositio Mathematica %D 1990 %P 1-30 %V 73 %N 1 %I Kluwer Academic Publishers %U http://www.numdam.org/item/CM_1990__73_1_1_0/ %G en %F CM_1990__73_1_1_0
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://www.numdam.org/item/CM_1990__73_1_1_0/
[Ba] The Multiplicities of Certain K-types in Irreducible Spherical Representations of Semisimple Lie Groups. Thesis Massachusetts Institute of Technology, 1987.
:[B-G] Tensor products of finite and infinite dimensional representations of semisimple Lie algebras. Comp. Math. 41 (1980), p. 245-285. | Numdam | MR | Zbl
and :[D-P] 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
Dijk & :[D] Enveloping Algebras. North-Holland Publishing Company, Amsterdam/ New York/Oxford, 1977. | MR | Zbl
:[Fa] Distributions sphériques sur les espaces hyperboliques. J. Math. Pures et Appl. 58 (1979), p. 369-444. | MR | Zbl
:[F-K] 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] A Duality for Symmetric Spaces with Applications to Group Representations I. Adv. Math. 5 (1970), p. 1-154. | MR | Zbl
:[Kn] Representation Theory of Semisimple Groups. An Overview Based on Examples. Princeton University Press, Princeton N.J., 1986. | MR | Zbl
:[Ko] 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] Spherical distributions on rank one symmetric spaces. Thesis University of Leiden, 1983.
:[MKo-D] 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] 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] 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] Harmonic Analysis on SL(n, R)/GL(n - 1, R). Thesis University of Utrecht, 1986.
:[T] 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] Harmonic Analysis on Real Reductive Groups. Lecture Notes in Mathematics, No. 576, Springer-Verlag, Berlin/ Heidelberg/New York, 1977. | MR | Zbl
:[Vo1] Representations of Real Reductive Lie Groups. Birkhäuser, Boston/ Basel/ Stuttgart, 1981. | MR | Zbl
:[Vo2] The unitary dual of GL(n) over an archimedian field. Invent. Math. 83 (1985), p. 449-505. | MR | Zbl
:[W] Harmonic Analysis on Homogeneous Spaces. Dekker, New-York, 1977. | MR | Zbl
:[Z] Tensor products of finite and infinite dimensional representations of semisimple Lie groups. Ann. Math. 106 (1977), p. 295-308. | MR | Zbl
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