Bulletin of the American Mathematical Society

MathSciNet review: 1567653
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Book Information:

Author: Anthony W. Knapp
Title: Representation theory of semisimple groups. An overview based on examples
Additional book information: Princeton Mathematics Series, vol. 36, Princeton University Press, Princeton, N. J., 1986, xvii + 773 pp., $75.00. ISBN 0-691-08401-7.

Michael Atiyah and Wilfried Schmid, A geometric construction of the discrete series for semisimple Lie groups, Invent. Math. 42 (1977), 1–62. MR 463358, DOI 10.1007/BF01389783

V. Bargmann, Irreducible unitary representations of the Lorentz group, Ann. of Math. (2) 48 (1947), 568–640. MR 21942, DOI 10.2307/1969129

Armand Borel and Nolan R. Wallach, Continuous cohomology, discrete subgroups, and representations of reductive groups, Annals of Mathematics Studies, No. 94, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1980. MR 554917

François Bruhat, Sur les représentations induites des groupes de Lie, Bull. Soc. Math. France 84 (1956), 97–205 (French). MR 84713

Mogens Flensted-Jensen, Discrete series for semisimple symmetric spaces, Ann. of Math. (2) 111 (1980), no. 2, 253–311. MR 569073, DOI 10.2307/1971201

I. M. Gel′fand and M. A. Naĭmark, Unitary representations of the Lorentz group, Izvestiya Akad. Nauk SSSR. Ser. Mat. 11 (1947), 411–504 (Russian). MR 0024440

I. M. Gel′fand and M. A. Naĭmark, Unitarnye predstavleniya klassičeskih grupp, Izdat. Nauk SSSR, Moscow-Leningrad, 1950 (Russian). Trudy Mat. Inst. Steklov. no. 36,. MR 0046370

Harish-Chandra, Discrete series for semisimple Lie groups. I. Construction of invariant eigendistributions, Acta Math. 113 (1965), 241–318. MR 219665, DOI 10.1007/BF02391779

Harish-Chandra, Discrete series for semisimple Lie groups. II. Explicit determination of the characters, Acta Math. 116 (1966), 1–111. MR 219666, DOI 10.1007/BF02392813

Rebecca A. Herb, Fourier inversion and the Plancherel theorem for semisimple real Lie groups, Amer. J. Math. 104 (1982), no. 1, 9–58. MR 648480, DOI 10.2307/2374067

V. S. Varadarajan, Harmonic analysis on real reductive groups, Lecture Notes in Mathematics, Vol. 576, Springer-Verlag, Berlin-New York, 1977. MR 0473111

David A. Vogan Jr., Representations of real reductive Lie groups, Progress in Mathematics, vol. 15, Birkhäuser, Boston, Mass., 1981. MR 632407

13.

G. Warner, Harmonic analysis on semisimple Lie groups, vols. I and II, Springer-Verlag, Berlin, and New York, 1972.

H. Weyl, Theorie der Darstellung kontinuierlicher halb-einfacher Gruppen durch lineare Transformationen. I, Math. Z. 23 (1925), no. 1, 271–309 (German). MR 1544744, DOI 10.1007/BF01506234

E. Wigner, On unitary representations of the inhomogeneous Lorentz group, Ann. of Math. (2) 40 (1939), no. 1, 149–204. MR 1503456, DOI 10.2307/1968551

1.

M. Atiyah and W. Schmid, A geometric construction of the discrete series for semisimple Lie groups, Invent. Math. 42 (1977), 1-62. MR 0463358

2.

V. Bargmann, Irreducible unitary representations of the Lorentz group, Ann. of Math. (2) 48 (1947), 568-640. MR 21942

3.

A. Borel and N. Wallach, Continuous cohomology, discrete subgroups, and representations of reductive groups, Princeton Univ. Press, Princeton, N. J., 1980. MR 554917

4.

F. Bruhat, Sur les représentations induites des groupes de Lie, Bull. Soc. Math. France 84 (1956), 97-205. MR 84713

5.

M. Flensted-Jensen, Discrete series for semisimple symmetric spaces, Ann. of Math. (2) 111 (1980), 253-311. MR 569073

6.

I. M. Gelfand and M. A. Naimark, Unitary representations of the Lorentz group, Izv. Akad. Nauk SSSR 11 (1947), 411-504. MR 24440

7.

I. M. Gelfand and M. A. Naimark, Unitary representations of the classical groups, Trudy Mat. Inst. Steklov 36, Moscow-Leningrad, 1950. German translation: Akademie-Verlag, Berlin, 1957. MR 46370

8.

Harish-Chandra, Discrete series for semi-simple Lie groups. I, Construction of invariant eigendistributions, Acta Math. 113 (1965), 241-318. MR 219665

9.

Harish-Chandra, Discrete series for semi-simple Lie groups. II, Explicit determination of the characters, Acta Math. 116 (1966), 1-111. MR 219666

10.

R. Herb, Fourier inversion and the Plancherel theorem for semisimple real Lie groups, Amer. J. Math. 104 (1982), 9-58. MR 648480

11.

V. S. Varadarajan, Harmonic analysis on real reductive groups, Lecture Notes in Math., vol 576, Springer-Verlag, Berlin and New York, 1977. MR 473111

12.

D. Vogan, Representations of real reductive Lie groups, Birkhäuser, Boston-Basel-Stuttgart, 1981. MR 632407

13.

G. Warner, Harmonic analysis on semisimple Lie groups, vols. I and II, Springer-Verlag, Berlin, and New York, 1972.

14.

H. Weyl, Theorie der Darstellung kontinuierlicher Gruppen. I, II, III, Math. Z. 23 (1925), 271-309; 24 (1925), 328-376, 377-395. MR 1544744

15.

E. Wigner, On unitary representations of the inhomogeneous Lorentz group, Ann. of Math. (2) 40 (1939), 149-204. MR 1503456