On Kirillov's conjecture for archimedean fields
Sahi, Siddhartha
Compositio Mathematica, Tome 72 (1989), p. 67-86 / Harvested from Numdam
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Publié le : 1989-01-01
@article{CM_1989__72_1_67_0,
     author = {Sahi, Siddhartha},
     title = {On Kirillov's conjecture for archimedean fields},
     journal = {Compositio Mathematica},
     volume = {72},
     year = {1989},
     pages = {67-86},
     mrnumber = {1026329},
     zbl = {0693.22006},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CM_1989__72_1_67_0}
}

Sahi, Siddhartha. On Kirillov's conjecture for archimedean fields. Compositio Mathematica, Tome 72 (1989) pp. 67-86. http://gdmltest.u-ga.fr/item/CM_1989__72_1_67_0/

[B] J. Bernstein, P-invariant distribution on GL(n) and the classification of unitary representations of GL(n) (non-Archimedean case), in Lie Group Representations II, Proceedings, University of Maryland (1982-1983). | MR 748505 | Zbl 0541.22009

[BZ] J. Bernstein and A. Zelevinsky, Induced representations of reductive p-adic groups I, Ann. Scient. Ec. Norm. Sup. 10 (1977) 441-472. | Numdam | MR 579172 | Zbl 0412.22015

[Ge] S. Gelbart, Fourier Analysis on Matrix Space, Mem. Amer. Math. Soc. No. 108 (1971). | MR 492066 | Zbl 0227.43016

[H] R. Howe, On a notion of rank for unitary representations of the classical groups, Harmonic Analysis and Group Representations, Proceedings, C.I.M.E. II ciclo 1980, Liguori Editore, Naples (1980). | MR 777342

[K] A.A. Kirillov, Infinite-dimensional representations of the general linear group, Dokl. Akad. Nauk SSSR 144 (1962) 36-39(= Soviet Math. Dokl. 3 (1962) 652-655). | MR 139691 | Zbl 0119.26804

[KS] A. Knapp and E. Stein, Intertwining operators for SL (n, R), Essays in Honor of Valentine Bargmann, Studies in Mathematical Physics, Princeton University Press, Princeton, New Jersey (1976). | Zbl 0334.22011

[L] S. Lang, SL (2, R), Addison-Wesley Publishing Company, Reading, Massachusetts (1975). | Zbl 0311.22001

[M] G. Mackey, Induced representations of locally compact groups I, Ann. of Math. 55 (1952) 101-139. | MR 44536 | Zbl 0046.11601

[S] S. Sahi, A simple construction of Stein's complementary series representations, to appear in Proc. Amer. Math. Soc. | MR 984813 | Zbl 0714.22013

[Sc] R. Scaramuzzi, Unitary representations of small rank of general linear groups, Ph.D. dissertation, Yale University, New Haven, Connecticut (1985).

[St] E. Stein, Analysis in matrix space and some new representations of SL(n, C), Ann. of Math. 86 (1967) 461-490. | MR 219670 | Zbl 0188.45303

[T] M. Tadic, Solution of the unitarizability problem for the general linear group (non-archimedean case), Ann, Scient. Ec. Norm. Sup. 19 (1986) 335-382. | Numdam | Zbl 0614.22005

[T1] M. Tadic, Unitary representations of the general linear group over the real and complex fields, preprint.

[V] D. Vogan, The unitary dual of GL(n) over an archimedean field, Invent. Math. 83 (1986) 449-505. | MR 827363 | Zbl 0598.22008

[W] N. Wallach, Cyclic vectors and irreducibility for principal series representations, Trans. Amer. Math. Soc. 158 (1971) 107-113. | MR 281844 | Zbl 0227.22016

[Wr] G. Warner, Harmonic Analysis on Semi-Simple Lie Groups I, Springer-Verlag, Berlin- Heidelberg- New York (1972). | MR 498999 | Zbl 0265.22020