Unitary representations with non-zero cohomology

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1. [1] M.W. Baldoni-Silva and D. Barbasch: The unitary spectrum for real rank one groups. Invent. Math.72 (1983) 27-55. Zbl0561.22009MR696689
2. [2] A. Borel and N. Wallach: Continuous cohomology, discrete subgroups, representations of reductive groups, Princeton University Press, Princeton, New Jersey (1980). Zbl0443.22010MR554917
3. [3] W. Casselman and M.S. Osborne: The n-cohomology of representations with an infinitesimal character. Comp. Math.31 (1975) 219-227. Zbl0343.17006MR396704
4. [4] T. Enright: Relative Lie algebra cohomology and unitary representations of complex Lie groups. Duke Math. J.46 (1979) 513-525. Zbl0427.22010MR544243
5. [5] A. Guichardet: Cohomologie des groupes topologiques et des algèbres de Lie, CEDIC-Fernand Nathan, Paris (1980). Zbl0464.22001MR644979
6. [6] Harish-Chandra: Representations of semi-simple Lie groups I. Trans. Amer. Math. Soc.75 (1953) 185-243. Zbl0051.34002MR56610
7. [7] S. Helgason: Differential Geometry, Lie Groups, and Symmetric Spaces. Academic Press, New York (1978). Zbl0451.53038MR514561
8. [8] R. Hotta and R. Parthasarathy: A geometric meaning of the multiplicities of integrable discrete classes in L2(Γ). Osaka J. Math.10 (1973) 211-234. Zbl0337.22016
9. [9] J. Humphreys: Introduction to Lie algebras and representation theory. Springer-Verlag, New YorkHeidelbergBerlin (1972). Zbl0254.17004MR323842
10. [10] S. Kumaresan: The canonical f-types of the irreducible unitary g-modules with non-zero relative cohomology. Invent. Math.59 (1980) 1-11. Zbl0442.22010MR575078
11. [11] R. Parthasarathy: Dirac operator and the discrete series. Ann. Math.96 (1972) 1-30. Zbl0249.22003MR318398
12. [12] R. Parthasarathy: A generalization of the Enright-Varadarajan modules. Comp. Math.36 (1978) 53-73. Zbl0384.17005MR515037
13. [13] R. Parthasarathy: Criteria for the unitarizability of some highest weight modules. Proc. Indian Acad. Sci.89 (1980) 1-24.. Zbl0434.22011MR573381
14. [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. Zbl0177.18004MR225936
15. [15] B. Speh: Unitary representations of GL(n, R) with non-trivial (g, K ) cohomology. Invent. Math.71 (1983) 443-465. Zbl0505.22015MR695900
16. [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 Mathematics880, Springer-Verlag, BerlinHeidelbergNew York (1981). Zbl0516.22008MR644844
17. [17] B. Speh and D. Vogan: Reducibility of generalized principal series representations. Acta Math.145 (1980) 227-299. Zbl0457.22011MR590291
18. [18] D. Vogan: The algebraic structure of the representations of semi-simple Lie groups I. Ann. Math.109 (!979) 1-60. Zbl0424.22010MR519352
19. [19] D. Vogan: Representations of real reductive Lie groups, Birkhäuser, Boston-Vasel-Stuttgart (1981). Zbl0469.22012MR632407
20. [20] G. Warner: Harmonic analysis on semi-simple Lie groups I, Springer-Verlag, BerlinHeidelbergNew York (1972). Zbl0265.22020MR498999
21. [21] J. Rawnsley, W. Schmid and J. Wolf: Singular unitary representations and indefinite harmonic theory, to appear in J. Func. Anal., 1983. Zbl0511.22005MR699229

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