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).


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
Full Text: DOI


[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.