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Complex manifolds whose skeletons are semisimple real Lie groups and analytic discrete series representations. (English. Russian original) Zbl 0449.22018

Funct. Anal. Appl. 11, 258-265 (1978); translation from Funkts. Anal. Prilozh. 11, No. 4, 19-27 (1977).

MSC:

22E46 Semisimple Lie groups and their representations
32M15 Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects)
32C05 Real-analytic manifolds, real-analytic spaces
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References:

[1] V. Bargmann, ”Irreducible unitary representations of the Lorentz group,” Ann. Math.,48, 568-640 (1947). · Zbl 0045.38801 · doi:10.2307/1969129
[2] Harish-Chandra, ”Representations of semisimple Lie groups. VI,” Am. J. Math.,78, 564-628 (1956). · Zbl 0072.01702 · doi:10.2307/2372674
[3] S. Lang, SL2 (R), Addison-Wesley (1975).
[4] I. M. Gel’fand, M. I. Graev, and I. I. Pyatetskii-Shapiro, Representation Theory and Automorphic Functions, Saunders (1969).
[5] S. Bochner, ”Group invariance of Cauchy’s formula in several variables,” Ann. Math.,45, 686-707 (1944). · Zbl 0060.24301 · doi:10.2307/1969297
[6] S. G. Gindikin, ”Analysis in homogeneous spaces,” Usp. Mat. Nauk,19, No. 4, 3-92 (1964). · Zbl 0144.08101
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