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ISSN 1088-9485(e) ISSN 0273-0979(p)

Book Review

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Book Information

Author(s): M. A. Naĭmark and A. I. Štern
Title: Theory of group representations
Additional book information: translated by Elizabeth Hewitt, translation edited by Edwin Hewitt, Grundlehren der mathematischen Wissenschaften, vol. 246, Springer-Verlag, Berlin, Heidelberg, and New York, 1982, ix + 568 pp., $59.00. ISBN 0-3879-0602-9

References:

1.: R. Bott, The index theorem for homogeneous differential operators, (S. S. Cairns, ed.), Differential and Combinatorial Topology: A Symposium in Honor of Marston Morse, Princeton Univ. Press, Princeton, N.J., 1965, pp. 167-186. MR 182022
2.: J. Dieudonné, Treatise on analysis, vol. 5, Academic Press, New York, 1977, Chapter 21. MR 467782
3.: J. Dieudonné, Special functions and linear representations of Lie groups, CBMS Regional Conf. Ser. in Math., No. 42, Amer. Math. Soc., Providence, R.I., 1980. MR 557540
4.: F. G. Frobenius, Gesammelte Abhandlungen, vol. 3, J.-P. Serre, ed., Springer-Verlag, Berlin, Heidelberg, and New York, 1968, pp. 1-166. See also I. Schur, Gesammelte Abhandlungen, vol. 1, A. Brauer and H. Rohrbach, eds., Springer-Verlag, Berlin, Heidelberg, and New York, 1973, pp. 1-169. MR 235974
5.: S. Helgason, Topics in harmonic analysis on homogeneous spaces, Birkhäuser, Boston and Basel, 1981. MR 632696
6.: E. Hewitt and K. A. Ross, Abstract harmonic analysis, vol. 2, 2nd ed., Springer-Verlag, Berlin, Heidelberg, and New York, 1979. MR 551496
7.: R. Howe, On the role of the Heisenberg group in harmonic analysis, Bull. Amer. Math. Soc. (N.S.) 3 (1980), 821-843. MR 578375
8.: W. Y. Hsiang, Cohomology theory of topological transformation groups, Springer-Verlag, Berlin, Heidelberg, and New York, 1975. MR 423384
9.: J. E. Humphreys, Introduction to Lie algebras and representation theory, Springer-Verlag, Berlin, Heidelberg, and New York, 1972. MR 323842
10.: A. A. Kirillov, Elements of the theory of representations, transl. by E. Hewitt, Springer-Verlag, Berlin, Heidelberg, and New York, 1976. Original Russian ed., Nauka, Moscow, 1972; French ed., transl. by A. Sossinsky, Mir, Moscow, 1974. MR 412321
11.: A. W. Knapp, Review of Lie groups, Lie algebras, and their representations, by V. S. Varadarajan, and Compact Lie groups and their representations, by D. P. Želobenko, Bull. Amer. Math. Soc. 81 (1975), 865-872.
12.: S. Lang, SL₂(R), Addison-Wesley, Reading, Mass., 1975. MR 430163
13.: G. W. Mackey, Harmonic analysis as the exploitation of symmetry―a historical survey, Bull. Amer. Math. Soc. (N.S.) 3 (1980), 543-698.
14.: J.-P. Serre, Linear representations of finite groups, transl. by L. L. Scott, Springer-Verlag, Berlin, Heidelberg, and New York, 1977. Original French ed., Hermann, Paris, 1971. MR 450380
15.: V. S. Varadarajan, Lie groups, Lie algebras, and their representations, Prentice-Hall, Englewood Cliffs, N.J., 1974. MR 376938
16.: J. A. Wolf, Spaces of constant curvature, 4th ed., Publish or Perish, Berkeley, 1977. MR 928600
17.: D. P. Želobenko, Compact Lie groups and their representations, transl. by Israel Program for Sci. Transl., Transl. Math. Mono., vol. 40, Amer. Math. Soc., Providence, R.I., 1973. Original Russian ed., Nauka, Moscow, 1970. MR 473097

Additional Information:

Reviewer(s):
Jonathan Rosenberg

Review Information:
Journal: Bull. Amer. Math. Soc. 9 (1983), 115-121.
DOI: 10.1090/S0273-0979-1983-15178-9
PII: S 0273-0979(1983)15178-9

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