Book Review

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Book Information:

Author: Jr. A. W. Knapp and D. A. Vogan

Title: Cohomological induction and unitary representations

Additional book information: Princeton Univ. Press, Princeton, NJ, 1995, xvii +948 pp., ISBN 0-691-03756-6

**[Ba]**D. Barbasch,*The unitary dual for complex classical Lie groups*, Invent. Math.**96**(1989), 103-176.MR**90c:22044****[BL]**J. Bernstein and V. Lunts,*Equivariant sheaves and functors*, LNM, vol. 1578, Springer-Verlag, Berlin-Heidelberg-Tokyo, 1994. MR**95k:55012****[BZ]**L. Barchini and R. Zierau,*Square integrable harmonic forms and representation theory*, Duke Math. J.**92**, no. 3 (1998), 645-664. CMP**98:12****[EW]**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****[GGPS]**I. M. Gelfand, M. I. Graev, and I. I. Pyatetskii-Shapiro,*Representation theory and automorphic functions*, 1990, Academic Press. MR**91g:11052****[K]**A. Knapp,*Representation theory of semisimple groups*, Princeton Mathematical Series, vol. 36, 1986, Princeton University Press. MR**87j:22022****[Ku]**S. Kumaresan,*On the canonical -types in the irreducible unitary -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****[KV]**A. V. Klimyk and N. A. Vilenkin,*Representations of Lie groups and special functions*, Kluwer Academic Publishers, Dordrecht, Boston, 1991. MR**93h:33009****[M]**S. MacLane,*Homology*, Academic Press-Springer Verlag, New York, Berlin, Göttingen, 1963. MR**28:122****[MP]**D. Milicic and P. Pandzic,*Equivariant derived categories, Zuckerman functors and localization*, Geometry and representation theory of real and -adic groups, Progress in Mathematics, vol. 158, Birkhäuser-Boston, 1997, pp. 209-242. CMP**98:05****[S]**W. Schmid,*On a conjecture of Langlands*, Ann. of Math.**93**(1971), 1-43. MR**44:4149****[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****[W]**N. Wallach,*Real reductive groups*, I, II, Academic Press, Boston, 1988, 1992. MR**89i:22029**; MR**93m:22018****[Wo]**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**

Review Information:

Reviewer: Dan Barbasch

Affiliation: Cornell University

Email: barbasch@math.cornell.edu

Journal: Bull. Amer. Math. Soc.

**36**(1999), 391-397

MSC (1991): Primary 22-XX

DOI: https://doi.org/10.1090/S0273-0979-99-00782-X

Published electronically: April 21, 1999

Review copyright: © Copyright 1999 American Mathematical Society