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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(e) ISSN 0273-0979(p)
     

Book Review

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Book Information

Author(s): Roe Goodman and Nolan R. Wallach
Title: Representations and invariants of the classical groups
Additional book information: Cambridge Univ. Press, Cambridge, 1998, xvi + 685 pp., (hardcover) $100.00, ISBN 0-521-58273-3 ; (paperback) $39.95, ISBN 0-521-66348-2


References:

1.
L.C. Biedenharn and J.D. Louck, Angular Momentum in Quantum Physics, Theory and Application, (1981) Encyclopedia of Mathematics and Its Applications, G.-C. Rota, editor, vol. 8, Addison-Wesley Publishing Company, Reading, Mass. MR 83a:81001

2.
H. Boerner, Representations of Groups with Special Consideration for the Needs of Modern Physics, (1970) North Holland, New York. MR 42:7792

3.
A. Borel, Linear Algebraic Groups, (1969) W.A. Benjamin, New York. MR 40:4273

4.
T. Bröcker and T. tomDieck, Representations of Compact Lie Groups, (1985) Graduate Texts in Mathematics 98, Springer-Verlag (New York, Berlin, Heidelberg, Tokyo). MR 86i:22023

5.
A. Cayley, A Second Memoir upon Quantics, CLXVI (1856) Philosophical Transactions of the Royal Society of London [Collected Works, Vol. II (1889), Cambridge at the University Press (141), pp. 533-538].

6.
A. Clebsch and F. Lindemann, Vorlesungen über Geometrie, (1876-1891) Leipzig.

7.
J. Dixmier, Quelques aspects de la théorie des invariants 43 (1990), Gazette des Math., 39-64. MR 90m:15047

8.
J. Dixmier and D. Lazard, Le Nombre Minimum d'Invariants Fondamentaux Pour Les Formes Binaires de Degré 7, 43 (1985-1986) Portugaliae Mathematica. MR 88f:15045

9.
E.B. Elliott, An Introduction to the Algebra of Quantics, 1895, Oxford at the Clarendon Press.

10.
W. Fulton and J. Harris, Representation Theory: A First Course, (1991) Graduate Texts in Mathematics 129, Springer-Verlag, (New York, Berlin, Heidelberg). MR 93a:20069

11.
H. Freudenthal and H. de Vries, Linear Lie Groups, (1969) Academic Press, New York. MR 41:5546

12.
F. von Gall, Das vollständige Formensystem der binären Formen 7ten Ordnung, 31 (1888) Math. Ann., 318-336.

13.
O.E. Glenn, A Treatise on the Theory of Invariants, (1915) Ginn and Company, Boston.

14.
P. Gordan, Vorlesungen über Invariantentheorie, (ed. G. Kerschensteiner) Vol. 1 (1885), Vol. 2 (1887) Leipzig, 2nd Edition (1987) Chelsea Publishing Company, New York. MR 89g:01034

15.
J.H. Grace and A. Young, The Algebra of Invariants, (1903) Cambridge University Press, (Reprinted Chelsea Publishing Company, Bronx, New York).

16.
S. Helgason, Differential Geometry, Lie Groups and Symmetric Spaces, (1978) Pure and Applied Math. 80, Academic Press, NY. MR 80k:53081

17.
R. Howe, Perspectives on Invariant Theory, The Schur Lectures (1992) (ed., I. Piatetski-Shapiro and S. Gelbart), Israel Mathematical Conference Proceedings 8. MR 96e:13006

18.
R. Howe, The first fundamental theorem of invariant theory and spherical subgroups, (333-346), Vol. 56 Part One, Proc. of Summer Research Institute on Algebraic Groups and Their Generalizations, (1991) (Eds. Haboush and Parshall), Proceedings of Symposia in Pure Mathematics, AMS, Providence, Rhode Island. MR 95f:13008

19.
J.E. Humphreys, Introduction to Lie Algebras and Representation Theory (1972) Springer-Verlag. MR 48:2197

20.
N. Jacobson, Lie Algebras, (1962) Wiley-Interscience, New York (Reprinted Dover 1979). MR 80k:17001

21.
D. Mumford and J. Fogarty, Geometric Invariant Theory, 2nd edition (1982) Ergebnisse der Math. und Ihrer Grenzgebiete 34, Springer-Verlag (Berlin, Heidelberg, New York). MR 86a:14006

22.
P.J. Olver, Equivalence, Invariants and Symmetry, (1995) Cambridge University Press. MR 96i:58005

23.
G. Salmon, A Treatise on Higher Plane Curves, 3rd Edition (1889), Hodges, Foster and Figgis, Dublin.

24.
G. Salmon, Lessons Introductory to the Modern Higher Algebra, 3rd Edition, (1885), Hodges, Foster and Figgis, Dublin.

25.
I. Schur (H. Grunsky), Vorlesungen über Invariantentheorie, (1968) Springer-Verlag. MR 37:5248

26.
T. Shioda, On the graded ring of invariants of binary octavics, 89 (1967) Amer. J. Math., 1022-1046. MR 36:3790

27.
J. Tits, Tabellen zu den einfachen Lie Gruppen und ihren Darstellungen, (1967) Lecture Notes in Math. 40, Springer-Verlag, Berlin. MR 36:1575

28.
H.W. Turnbull, The Theory of Determinants, Matrices and Invariants, (1929) Blackie (London, Glasgow).

29.
V.S. Varadarajan, Lie Groups, Lie algebras and Their Representations, (1974; 1984) Graduate Texts in Math. 102, Springer-Verlag, New York. MR 51:13113; MR 85e:22001

30.
N.R. Wallach, Harmonic Analysis on Homogeneous Spaces, (1973) Marcel Dekker, Inc., New York. MR 58:16978

31.
H. Weyl, The Classical Groups, Their Invariants and Representations (First Edition, 1939, Second Edition with supplements, 1946) Princeton University Press. MR 1:42c; MR 98k:01049

32.
A. Young, Collected Papers, Univ. of Toronto Press Math. Expositions, no. 21 (1977), Univ. of Toronto Press. MR 55:12438

33.
D.P. \v{Z}elobenko, Compact Lie Groups and Their Representations, (1973) Translations of Mathematical Monographs 40, Amer. Math. Soc., Providence, RI. MR 57:12776b


Additional Information:

Reviewer(s):
Jacob Towber
Affiliation: De Paul University
Email: jtowber@math.uchicago.edu

Review Information:
Journal: Bull. Amer. Math. Soc. 36 (1999), 533-538.

MSC (1991): Primary 20G20, 22E46
DOI: 10.1090/S0273-0979-99-00795-8
PII: S 0273-0979(99)00795-8
Posted: July 28, 1999
Copyright of article: Copyright 1999, American Mathematical Society


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