Unitary representations with non-zero cohomology
Vogan, David A. ; Zuckerman, Gregg J.
Compositio Mathematica, Tome 53 (1984), p. 51-90 / Harvested from Numdam
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@article{CM_1984__53_1_51_0,
     author = {Vogan, David A. and Zuckerman, Gregg J.},
     title = {Unitary representations with non-zero cohomology},
     journal = {Compositio Mathematica},
     volume = {53},
     year = {1984},
     pages = {51-90},
     mrnumber = {762307},
     zbl = {0692.22008},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CM_1984__53_1_51_0}
}

Vogan, David A.; Zuckerman, Gregg J. Unitary representations with non-zero cohomology. Compositio Mathematica, Tome 53 (1984) pp. 51-90. http://gdmltest.u-ga.fr/item/CM_1984__53_1_51_0/

[1] M.W. Baldoni-Silva and D. Barbasch: The unitary spectrum for real rank one groups. Invent. Math. 72 (1983) 27-55. | MR 696689 | Zbl 0561.22009

[2] A. Borel and N. Wallach: Continuous cohomology, discrete subgroups, representations of reductive groups, Princeton University Press, Princeton, New Jersey (1980). | MR 554917 | Zbl 0443.22010

[3] W. Casselman and M.S. Osborne: The n-cohomology of representations with an infinitesimal character. Comp. Math. 31 (1975) 219-227. | Numdam | MR 396704 | Zbl 0343.17006

[4] T. Enright: Relative Lie algebra cohomology and unitary representations of complex Lie groups. Duke Math. J. 46 (1979) 513-525. | MR 544243 | Zbl 0427.22010

[5] A. Guichardet: Cohomologie des groupes topologiques et des algèbres de Lie, CEDIC-Fernand Nathan, Paris (1980). | MR 644979 | Zbl 0464.22001

[6] Harish-Chandra: Representations of semi-simple Lie groups I. Trans. Amer. Math. Soc. 75 (1953) 185-243. | MR 56610 | Zbl 0051.34002

[7] S. Helgason: Differential Geometry, Lie Groups, and Symmetric Spaces. Academic Press, New York (1978). | MR 514561 | Zbl 0451.53038

[8] R. Hotta and R. Parthasarathy: A geometric meaning of the multiplicities of integrable discrete classes in L2(Γ\G). Osaka J. Math. 10 (1973) 211-234. | Zbl 0337.22016

[9] J. Humphreys: Introduction to Lie algebras and representation theory. Springer-Verlag, New York Heidelberg Berlin (1972). | MR 323842 | Zbl 0254.17004

[10] S. Kumaresan: The canonical f-types of the irreducible unitary g-modules with non-zero relative cohomology. Invent. Math. 59 (1980) 1-11. | MR 575078 | Zbl 0442.22010

[11] R. Parthasarathy: Dirac operator and the discrete series. Ann. Math. 96 (1972) 1-30. | MR 318398 | Zbl 0249.22003

[12] R. Parthasarathy: A generalization of the Enright-Varadarajan modules. Comp. Math. 36 (1978) 53-73. | Numdam | MR 515037 | Zbl 0384.17005

[13] R. Parthasarathy: Criteria for the unitarizability of some highest weight modules. Proc. Indian Acad. Sci. 89 (1980) 1-24.. | MR 573381 | Zbl 0434.22011

[14] K.R. Parthasarathy, R. Ranga Rao and V.S. Varadarajan: Representations of complex semi-simple Lie groups and Lie algebras. Ann. Math. 85 (1967) 383-429. | MR 225936 | Zbl 0177.18004

[15] B. Speh: Unitary representations of GL(n, R) with non-trivial (g, K ) cohomology. Invent. Math. 71 (1983) 443-465. | MR 695900 | Zbl 0505.22015

[16] B. Speh: Unitary representations of SL(n, R) and the cohomology of congruence subgroups, In. Noncommutative Harmonic Analysis and Lie Groups, Lecture Notes in Mathematics 880, Springer-Verlag, Berlin Heidelberg New York (1981). | MR 644844 | Zbl 0516.22008

[17] B. Speh and D. Vogan: Reducibility of generalized principal series representations. Acta Math. 145 (1980) 227-299. | MR 590291 | Zbl 0457.22011

[18] D. Vogan: The algebraic structure of the representations of semi-simple Lie groups I. Ann. Math. 109 (!979) 1-60. | MR 519352 | Zbl 0424.22010

[19] D. Vogan: Representations of real reductive Lie groups, Birkhäuser, Boston-Vasel-Stuttgart (1981). | MR 632407 | Zbl 0469.22012

[20] G. Warner: Harmonic analysis on semi-simple Lie groups I, Springer-Verlag, Berlin Heidelberg New York (1972). | MR 498999 | Zbl 0265.22020

[21] J. Rawnsley, W. Schmid and J. Wolf: Singular unitary representations and indefinite harmonic theory, to appear in J. Func. Anal., 1983. | MR 699229 | Zbl 0511.22005