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Book Review

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Book Information

Author(s): 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, $65.00, 0-8218-3530-0

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L. Auslander and B. Kostant, Polarization and unitary representations of solvable Lie groups, Invent. Math. 14 (1971), 255-354. MR 0293012 (45:2092)

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V. Bargmann, Irreducible unitary representations of the Lorentz group, Ann. of Math. 48 (1947), 568-640. MR 0021942 (9:133a)

[DHV]
M. Duflo, G. Heckman, and M. Vergne, Projection d'orbites, formule de Kirillov et formule de Blattner, Harmonic analysis on Lie groups and symmetric spaces (Kleebach, 1983), Mém. Soc. Math. France (N.S.), No. 15, 1984, pp. 65-128. MR 0789081 (86m:22017)

[GN1]
I. M. Gelfand and M. A. Naimark, Unitary representations of the Lorentz group, Izv. Akad. Nauk S.S.S.R. 11 (1947), 411-504. MR 0024440 (9:495a)

[GN2]
I. M. Gelfand and M. A. Naimark, Unitary Representations of the Classical Groups, Trudy Mat. Inst. Steklov, vol. 36, Moscow-Leningrad, 1950; German transl.: Akademie-Verlag, Berlin, 1957. MR 0046370 (13:722f)

[GV]
W. Graham and D. Vogan, Geometric quantization for nilpotent coadjoint orbits, Geometry and Representation Theory of Real and $p$-adic Groups (J. Tirao, D. Vogan, and J. Wolf, eds.), Birkhäuser, Boston-Basel-Berlin, 1998, pp. 69-137. MR 1486137 (2000i:22024)

[He]
R. Hermann, Toda lattices, cosymplectic manifolds, Bäcklund transformations and kinks. Part A., Interdisciplinary Mathematics, Vol. XV, Math. Sci. Press, Brookline, MA, 1977. MR 0478194 (57:17682)

[Ki1]
A. Kirillov, Unitary representations of nilpotent Lie groups, Uspehi Mat. Nauk. 17 (1962), 57-110. MR 0142001 (25:5396)

[Ki2]
A. Kirillov, Elements of the Theory of Representations, English transl. by E. Hewitt, Springer-Verlag, Berlin-Heidelberg-New York, 1976. MR 0412321 (54:447)

[Ko]
B. Kostant, Quantization and unitary representations, Lectures in Modern Analysis and Applications (C. Taam, ed.), Lecture Notes in Mathematics, vol. 170, Springer-Verlag, Berlin-Heidelberg-New York, 1970, pp. 87-208. MR 0294568 (45:3638)

[La]
R. P. Langlands, On the functional equations satisfied by Eisenstein series, Lecture Notes in Mathematics, vol. 544, Springer-Verlag, Berlin-New York, 1976. MR 0579181 (58:28319)

[Lz]
A. Lichnerowicz, Les variétés de Poisson et leurs algèbres de Lie associées, J. Differential Geometry 12 (1977), 253-300. MR 0501133 (58:18565)

[So]
J.-M. Souriau, Structure des systèmes dynamiques, Maîtrises de mathématiques, Dunod, Paris, 1970; English transl. by C. H. Cushman-de Vries in Structure of Dynamical Systems: A Symplectic View of Physics, Progress in Mathematics, vol. 149, Birkhäuser Boston, Boston, MA, 1997. MR 0260238 (41:4866)

[St]
E. M. Stein, Analysis in matrix spaces and some new representations of SL(n, ${\mathbb{C}}$), Ann. of Math. (2) 86 (1967), 461-490. MR 0219670 (36:2749)

[V]
D. Vogan, The method of coadjoint orbits for real reductive groups, Representation Theory of Lie Groups, IAS/Park City Mathematics Series, vol. 8, American Mathematical Society, Providence, RI, 2000. MR 1737729 (2001k:22027)

[We]
A. Weinstein, The local structure of Poisson manifolds, J. Differential Geom. 18 (1983), 523-557. MR 0723816 (86i:58059)

Additional Information:

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

Review Information:
Journal: Bull. Amer. Math. Soc. 42 (2005), 535-544.

MSC (2000): Primary 22-02, 22E45
DOI: 10.1090/S0273-0979-05-01065-7
PII: S 0273-0979(05)01065-7
Posted: April 6, 2005
Copyright of article: Copyright 2005, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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