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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., $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).
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- 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
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- 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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