Bulletin of the American Mathematical Society

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Authors: 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.

Raoul Bott, The index theorem for homogeneous differential operators, Differential and Combinatorial Topology (A Symposium in Honor of Marston Morse), Princeton Univ. Press, Princeton, N.J., 1965, pp. 167–186. MR 0182022

J. Dieudonné, Treatise on analysis. Vol. 5. Chapter XXI, Pure and Applied Mathematics, Vol. 10-V, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1977. Translated by I. G. Macdonald. MR 0467782

Jean Dieudonné, Special functions and linear representations of Lie groups, CBMS Regional Conference Series in Mathematics, vol. 42, American Mathematical Society, Providence, R.I., 1980. Expository lectures from the CBMS Regional Conference held at East Carolina University, Greenville, North Carolina, March 5–9, 1979. MR 557540

Ferdinand Georg Frobenius, Gesammelte Abhandlungen. Bände I, II, III, Springer-Verlag, Berlin-New York, 1968 (German). Herausgegeben von J.-P. Serre. MR 0235974

Sigurdur Helgason, Topics in harmonic analysis on homogeneous spaces, Progress in Mathematics, vol. 13, Birkhäuser, Boston, Mass., 1981. MR 632696

Edwin Hewitt and Kenneth A. Ross, Abstract harmonic analysis. Vol. I, 2nd ed., Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 115, Springer-Verlag, Berlin-New York, 1979. Structure of topological groups, integration theory, group representations. MR 551496

Roger Howe, On the role of the Heisenberg group in harmonic analysis, Bull. Amer. Math. Soc. (N.S.) 3 (1980), no. 2, 821–843. MR 578375, DOI 10.1090/S0273-0979-1980-14825-9

Wu-yi Hsiang, Cohomology theory of topological transformation groups, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 85, Springer-Verlag, New York-Heidelberg, 1975. MR 0423384

James E. Humphreys, Introduction to Lie algebras and representation theory, Graduate Texts in Mathematics, Vol. 9, Springer-Verlag, New York-Berlin, 1972. MR 0323842

A. A. Kirillov, Elements of the theory of representations, Grundlehren der Mathematischen Wissenschaften, Band 220, Springer-Verlag, Berlin-New York, 1976. Translated from the Russian by Edwin Hewitt. MR 0412321

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.

Serge Lang, $\textrm {SL}_{2}(\textbf {R})$, Addison-Wesley Publishing Co., Reading, Mass.-London-Amsterdam, 1975. MR 0430163

13.

G. W. Mackey, Harmonic analysis as the exploitation of symmetry―a historical survey, Bull. Amer. Math. Soc. (N.S.) 3 (1980), 543-698.

Jean-Pierre Serre, Linear representations of finite groups, Graduate Texts in Mathematics, Vol. 42, Springer-Verlag, New York-Heidelberg, 1977. Translated from the second French edition by Leonard L. Scott. MR 0450380

V. S. Varadarajan, Lie groups, Lie algebras, and their representations, Prentice-Hall Series in Modern Analysis, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1974. MR 0376938

Joseph A. Wolf, Spaces of constant curvature, 5th ed., Publish or Perish, Inc., Houston, TX, 1984. MR 928600

D. P. Zhelobenko, Kompaktnye gruppy Li i ikh predstavleniya, Izdat. “Nauka”, Moscow, 1970 (Russian). MR 0473097

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 0182022

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