Book Review
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MathSciNet review:
1567223
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Book Information:
Author:
T. A. Springer
Title:
Invariant theory
Additional book information:
Lecture Notes in Math., vol. 585, Springer-Verlag, Berlin, Heidelberg, New York, 1977, 111 pp., $8.00.
1. G. Boole, Exposition of a general theory of linear transformations, Cambridge Math. J. 3 (1841), 1-20.
Claude Chevalley, Invariants of finite groups generated by reflections, Amer. J. Math. 77 (1955), 778–782. MR 72877, DOI 10.2307/2372597
Jean A. Dieudonné and James B. Carrell, Invariant theory, old and new, Advances in Math. 4 (1970), 1–80 (1970). MR 255525, DOI 10.1016/0001-8708(70)90015-0
Shiing Shen Chern, Geometry of characteristic classes, Proceedings of the Thirteenth Biennial Seminar of the Canadian Mathematical Congress (Dalhousie Univ., Halifax, N.S., 1971) Canad. Math. Congr., Montreal, Que., 1972, pp. 1–40. MR 0370613
Charles S. Fisher, The death of a mathematical theory. A study in the sociology of knowledge, Arch. History Exact Sci. 3 (1966), 137–159 (1966). MR 0202546, DOI 10.1007/BF00357267
Robert B. Gardner, The fundamental theorem of vector relative invariants, J. Algebra 36 (1975), no. 2, 314–318. MR 379518, DOI 10.1016/0021-8693(75)90107-6
Peter B. Gilkey, Curvature and the eigenvalues of the Laplacian for elliptic complexes, Advances in Math. 10 (1973), 344–382. MR 324731, DOI 10.1016/0001-8708(73)90119-9
W. J. Haboush, Reductive groups are geometrically reductive, Ann. of Math. (2) 102 (1975), no. 1, 67–83. MR 382294, DOI 10.2307/1970974
David Hilbert, Ueber die vollen Invariantensysteme, Math. Ann. 42 (1893), no. 3, 313–373 (German). MR 1510781, DOI 10.1007/BF01444162
10. D. Hilbert, Über die Theorie der Algebraischen Invarianten, International Mathematical Congress, Macmillan, New York, 1896, 116-124.
J. E. Humphreys, Hilbert’s fourteenth problem, Amer. Math. Monthly 85 (1978), no. 5, 341–353. MR 498068, DOI 10.2307/2321339
D. E. Littlewood, Invariant theory, tensors and group characters, Philos. Trans. Roy. Soc. London Ser. A 239 (1944), 305–365. MR 10594, DOI 10.1098/rsta.1944.0001
13. F. Meyer, Bericht über den gegenwärtigen Stand der Invariantentheorie, Jahresbericht der Deutschen Mathematiker-Vereinigung 1 (1890-1891).
David Mumford and Kalevi Suominen, Introduction to the theory of moduli, Algebraic geometry, Oslo 1970 (Proc. Fifth Nordic Summer-School in Math.), Wolters-Noordhoff, Groningen, 1972, pp. 171–222. MR 0437531
V. K. Patodi, An analytic proof of Riemann-Roch-Hirzebruch theorem for Kaehler manifolds, J. Differential Geometry 5 (1971), 251–283. MR 290318
C. Procesi, The invariant theory of $n\times n$ matrices, Advances in Math. 19 (1976), no. 3, 306–381. MR 419491, DOI 10.1016/0001-8708(76)90027-X
Steven M. Roman and Gian-Carlo Rota, The umbral calculus, Advances in Math. 27 (1978), no. 2, 95–188. MR 485417, DOI 10.1016/0001-8708(78)90087-7
18. G. C. Rota, P. Doubilet and M. Stern, On the foundations of combinatorial theory. IX, Studies in Applied Math. 17 (1974), 185-216.
Shiing-shen Chern and James Simons, Some cohomology classes in principal fiber bundles and their application to riemannian geometry, Proc. Nat. Acad. Sci. U.S.A. 68 (1971), 791–794. MR 279732, DOI 10.1073/pnas.68.4.791
N. J. A. Sloane, Error-correcting codes and invariant theory: new applications of a nineteenth-century technique, Amer. Math. Monthly 84 (1977), no. 2, 82–107. MR 424398, DOI 10.2307/2319929
Richard P. Stanley, Magic labelings of graphs, symmetric magic squares, systems of parameters, and Cohen-Macaulay rings, Duke Math. J. 43 (1976), no. 3, 511–531. MR 444514
Richard P. Stanley, Cohen-Macaulay rings and constructible polytopes, Bull. Amer. Math. Soc. 81 (1975), 133–135. MR 364231, DOI 10.1090/S0002-9904-1975-13670-6
Hermann Weyl, David Hilbert and his mathematical work, Bull. Amer. Math. Soc. 50 (1944), 612–654. MR 11274, DOI 10.1090/S0002-9904-1944-08178-0
Hermann Weyl, Invariants, Duke Math. J. 5 (1939), 489–502. MR 30
25. H. Weyl, Classical groups, Princeton Univ. Press, Princeton, N. J., 1939.
Hermann Weyl, On the Volume of Tubes, Amer. J. Math. 61 (1939), no. 2, 461–472. MR 1507388, DOI 10.2307/2371513
- 1.
- G. Boole, Exposition of a general theory of linear transformations, Cambridge Math. J. 3 (1841), 1-20.
- 2.
- C. Chevalley, Invariants of finite groups generated by reflections, Amer. J. Math. 67 (1955), 778-782. MR 0072877
- 3.
- J. Dieudonne and J. Carrell, Invariant theory old and new, Advances in Math. 4 (1970), 1-80. MR 255525
- 4.
- S. S. Chern, Geometry of characteristic classes, Proc. of 13th Biennial Seminar, Canad. Math. Soc., 1972, pp. 1-40. MR 370613
- 5.
- C. Fisher, The death of a mathematical theory, Arch. History Exact Sci. 3 (1966), 137-159. MR 202546
- 6.
- R. Gardner, The fundamental theorem of vector relative invariants, J. Algebra 36 (1975), 314-318. MR 379518
- 7.
- P. Gilkey, Curvature and the eigenvalues of the Laplacian for elliptic complexes, Advances in Math. 10 (1973), 344-382. MR 324731
- 8.
- W. Haboush, Reductive groups are geometrically reductive, Ann. of Math. (2) 102 (1975), 67-83. MR 382294
- 9.
- D. Hilbert, Über die vollen invariantensystem, Math. Ann. 42 (1893), 313-373. MR 1510781
- 10.
- D. Hilbert, Über die Theorie der Algebraischen Invarianten, International Mathematical Congress, Macmillan, New York, 1896, 116-124.
- 11.
- J. Humphreys, Hilbert's fourteenth problem, Amer. Math. Monthly 85 (1978), 341-353. MR 498068
- 12.
- D. Littlewood, Invariant thoery, tensors, and group characters, Phil. Trans. Royal Soc. 239 (1944), 305-365. MR 10594
- 13.
- F. Meyer, Bericht über den gegenwärtigen Stand der Invariantentheorie, Jahresbericht der Deutschen Mathematiker-Vereinigung 1 (1890-1891).
- 14.
- D. Mumford and T. Suominen, Introduction to the theory of moduli, Proc. of 5th Nordic Summer School, Wolters-Nordoff, Groningen, 1971, pp. 171-222. MR 437531
- 15.
- V. K. Patodi, An analytic proof of the Riemann-Roch-Hirzebruch theorem for Kahler manifolds, J. Differential Geometry 5 (1971), 251-283. MR 290318
- 16.
- C. Procesi, The invariant theory of n x n matrices, Advances in Math. 19 (1976), 306-381. MR 419491
- 17.
- G. C. Rota and S. Roman, The umbral calculus, Advances in Math. 27 (1978), 95-188. MR 485417
- 18.
- G. C. Rota, P. Doubilet and M. Stern, On the foundations of combinatorial theory. IX, Studies in Applied Math. 17 (1974), 185-216.
- 19.
- J. Simons and S. S. Chern, Some cohomology classes in principal fiber bundles and their application to Riemannian geometry, Proc. Nat. Acad. Sci. U.S.A. 68 (1971), 791-794. MR 279732
- 20.
- N. Sloane, Error connecting codes and invariant theory, Amer. Math. Monthly 84 (1977), 82-107. MR 424398
- 21.
- R. Stanley, Magic labelings of graphs, symmetric magic squares, systems of parameters, and Cohen-Macaulay rings, Duke Math. J. 43 (1976), 511-531. MR 444514
- 22.
- R. Stanley, Cohen-Macaulay rings and constructible polytopes, Bull. Amer. Math. Soc. 81 (1975), 133-155. MR 364231
- 23.
- H. Weyl, David Hilbert and his mathematical work, Bull. Amer. Math. Soc. 50 (1944), 612-654. MR 11274
- 24.
- H. Weyl, Invariants, Duke Math. J. 5 (1939), 489-502. MR 30
- 25.
- H. Weyl, Classical groups, Princeton Univ. Press, Princeton, N. J., 1939.
- 26.
- H. Weyl, On the volume of tubes, Amer. J. Math. 61 (1939), 461-472. MR 1507388
Review Information:
Reviewer:
Robert B. Gardner
Journal:
Bull. Amer. Math. Soc.
2 (1980), 246-256
DOI:
https://doi.org/10.1090/S0273-0979-1980-14739-4
