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Book Review

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Book Information:

Author: A. A. Kirillov
Title: Lectures on the orbit method
Additional book information: Graduate Studies in Mathematics, vol. 64, American Mathematical Society, Providence, RI, 2004, xx+408 pp., ISBN 0-8218-3530-0, $65.00$

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V. Bargmann, Irreducible unitary representations of the Lorentz group, Ann. of Math. (2) 48 (1947), 568–640. MR 21942, DOI 10.2307/1969129

Michel Duflo, Gerrit Heckman, and Michèle Vergne, Projection d’orbites, formule de Kirillov et formule de Blattner, Mém. Soc. Math. France (N.S.) 15 (1984), 65–128 (French, with English summary). Harmonic analysis on Lie groups and symmetric spaces (Kleebach, 1983). MR 789081

I. M. Gel′fand and M. A. Naĭmark, Unitary representations of the Lorentz group, Izvestiya Akad. Nauk SSSR. Ser. Mat. 11 (1947), 411–504 (Russian). MR 0024440

I. M. Gel′fand and M. A. Naĭmark, Unitarnye predstavleniya klassičeskih grupp, Izdat. Nauk SSSR, Moscow-Leningrad, 1950 (Russian). Trudy Mat. Inst. Steklov. no. 36,. MR 0046370

William Graham and David A. Vogan Jr., Geometric quantization for nilpotent coadjoint orbits, Geometry and representation theory of real and $p$-adic groups (Córdoba, 1995) Progr. Math., vol. 158, Birkhäuser Boston, Boston, MA, 1998, pp. 69–137. MR 1486137

Robert Hermann, Toda lattices, cosymplectic manifolds, Bäcklund transformations and kinks. Part A, Interdisciplinary Mathematics, Vol. XV, Math Sci Press, Brookline, Mass., 1977. MR 0478194

A. A. Kirillov, Unitary representations of nilpotent Lie groups, Uspehi Mat. Nauk 17 (1962), no. 4 (106), 57–110 (Russian). MR 0142001

A. A. Kirillov, Elements of the theory of representations, Grundlehren der Mathematischen Wissenschaften, Band 220, Springer-Verlag, Berlin-New York, 1976. Translated from the Russian by Edwin Hewitt. MR 0412321

Bertram Kostant, Quantization and unitary representations. I. Prequantization, Lectures in modern analysis and applications, III, Lecture Notes in Math., Vol. 170, Springer, Berlin, 1970, pp. 87–208. MR 0294568

Robert P. Langlands, On the functional equations satisfied by Eisenstein series, Lecture Notes in Mathematics, Vol. 544, Springer-Verlag, Berlin-New York, 1976. MR 0579181

André Lichnerowicz, Les variétés de Poisson et leurs algèbres de Lie associées, J. Differential Geometry 12 (1977), no. 2, 253–300 (French). MR 501133

J.-M. Souriau, Structure des systèmes dynamiques, Dunod, Paris, 1970 (French). Maîtrises de mathématiques. MR 0260238

E. M. Stein, Analysis in matrix spaces and some new representations of $\textrm {SL}(N,\,C)$, Ann. of Math. (2) 86 (1967), 461–490. MR 219670, DOI 10.2307/1970611

David A. Vogan Jr., The method of coadjoint orbits for real reductive groups, Representation theory of Lie groups (Park City, UT, 1998) IAS/Park City Math. Ser., vol. 8, Amer. Math. Soc., Providence, RI, 2000, pp. 179–238. MR 1737729, DOI 10.1090/pcms/008/05

Alan Weinstein, The local structure of Poisson manifolds, J. Differential Geom. 18 (1983), no. 3, 523–557. MR 723816

Review Information:

Reviewer: David A. Vogan, Jr.
Affiliation: Massachusetts Institute of Technology
Email: dav@math.mit.edu

Journal: Bull. Amer. Math. Soc. 42 (2005), 535-544
Published electronically: April 6, 2005
Review copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.