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Book Review

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Book Information

Author(s): A. W. Knapp and D. A. Vogan, Jr.
Title: Cohomological induction and unitary representations
Additional book information: Princeton Univ. Press, Princeton, NJ, 1995, xvii +948, 0-691-03756-6

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L. Barchini and R. Zierau, Square integrable harmonic forms and representation theory, Duke Math. J. 92, no. 3 (1998), 645-664. CMP 98:12

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T. Enright and N. Wallach, Notes on cohomological algebra and representations of Lie algebras, Duke Math. J. 47 (1980), 1-15. MR 81c:17013

[BW]
A. Borel and N. Wallach, Continuous cohomology, discrete subgroups and representations of reductive groups, Annals of Mathematics Studies, no. 94, 1980, Princeton University Press and University of Tokyo Press. MR 83c:22018

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I. M. Gelfand, M. I. Graev, and I. I. Pyatetskii-Shapiro, Representation theory and automorphic functions, 1990, Academic Press. MR 91g:11052

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A. Knapp, Representation theory of semisimple groups, Princeton Mathematical Series, vol. 36, 1986, Princeton University Press. MR 87j:22022

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S. Kumaresan, On the canonical $\mathfrak k$-types in the irreducible unitary $\mathfrak g$-modules with non-zero relative cohomology, Invent. Math. 59 (1980), 1-11. MR 83c:17011

[H]
S. Helgason, Differential geometry, Lie groups and symmetric spaces, Academic Press, 1978. MR 80k:53081

[HMSW]
H. Hecht, D. Milicic, W. Schmid, and J. Wolf, Localization and standard modules for real semisimple groups. I, Invent. Math. 90 (1987), 297-332. MR 89e:22025

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A. V. Klimyk and N. A. Vilenkin, Representations of Lie groups and special functions, Kluwer Academic Publishers, Dordrecht, Boston, 1991. MR 93h:33009

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S. MacLane, Homology, Academic Press-Springer Verlag, New York, Berlin, Göttingen, 1963. MR 28:122

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D. Milicic and P. Pandzic, Equivariant derived categories, Zuckerman functors and localization, Geometry and representation theory of real and $p$-adic groups, Progress in Mathematics, vol. 158, Birkhäuser-Boston, 1997, pp. 209-242. CMP 98:05

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[V1]
D. Vogan, Representations of real reductive groups, Progress in Mathematics, 1981, Birkhäuser, Boston-Basel-Stuttgart. MR 83c:22022

[V2]
D. Vogan, Unitarizability of certain series of representations, Ann. Math. 120 (1984), 141-187. MR 86h:22028

[VZ]
D. Vogan and G. Zuckerman, Unitary representations with nonzero cohomology, Comp. Math. 53 (1984), 51-90. MR 86k:22040

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N. Wallach, Real reductive groups, I, II, Academic Press, Boston, 1988, 1992. MR 89i:22029; MR 93m:22018

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H. Wong, Dolbeault cohomological realization of Zuckerman modules associated with finite rank representations, J. Funct. Anal. 129, no. 2 (1995), 428-454. MR 96c:22024

Additional Information:

Reviewer(s):
Dan Barbasch
Affiliation: Cornell University
Email: barbasch@math.cornell.edu

Review Information:
Journal: Bull. Amer. Math. Soc. 36 (1999), 391-397.

MSC (1991): Primary 22-XX
DOI: 10.1090/S0273-0979-99-00782-X
PII: S 0273-0979(99)00782-X
Posted: April 21, 1999
Copyright of article: Copyright 1999, American Mathematical Society

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