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Hermitian symmetric spaces and their unitary highest weight modules. (English) Zbl 0517.22014


MSC:

22E46 Semisimple Lie groups and their representations
32M15 Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects)
22E47 Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.)
17B20 Simple, semisimple, reductive (super)algebras
17B35 Universal enveloping (super)algebras

Citations:

Zbl 0478.22007
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Full Text: DOI

References:

[1] Bernstein, I. N.; Gelfand, I. M.; Gelfand, S. I., Differential operators on the base affine space and a study of g-modules, (Gelfand, I. M., Lie Groups and Their Representations (1975), Adam Hilger: Adam Hilger London) · Zbl 0338.58019
[2] Cartan, É., Sur les domaines bornés homogènes de l’espace de \(n\) variables complexes, (Abh. Math. Sem. Univ. Hamburg, 11 (1935)), 116-162
[3] Enright, T. J.; Parthasarathy, R., A proof of a conjecture of Kashiwara and Vergne, (Non Commutative Harmonic Analysis and Lie Groups. Non Commutative Harmonic Analysis and Lie Groups, Lecture Notes in Math. No. 880 (1981), Springer: Springer Berlin/Heidelberg/New York) · Zbl 0492.22012
[4] Jakobsen, H. P.; Vergne, M., Restrictions and expansions of holomorphic representations, J. Funct. Anal., 34, 29-53 (1979) · Zbl 0433.22011
[5] Jakobsen, H. P., On singular holomorphic representations, Invent. Math., 62, 67-78 (1980) · Zbl 0466.22016
[6] Jakobsen, H. P., The last possible place of unitarity for certain highest weight modules, Math. Ann., 256, 439-447 (1981) · Zbl 0478.22007
[7] Kashiwara, M.; Vergne, M., On the Segal-Shale-Weil representation and harmonic polynomials, Invent. Math., 44, 1-47 (1978) · Zbl 0375.22009
[8] Rossi, H.; Vergne, M., Analytic continuation of the holomorphic discrete series of a semi-simple Lie group, Acta Math., 136, 1-59 (1976) · Zbl 0356.32020
[9] Wallach, N., Analytic continuation of the discrete series II, Trans. Amer. Math. Soc., 251, 19-37 (1979) · Zbl 0419.22018
[11] Garland, H.; Zuckerman, G. J., On unitarizable highest weight modules of Hermitian pairs, J.Fac. Sci. Univ. Tokyo Sect. IA Math., 28, 877-889 (1982) · Zbl 0499.17004
[13] Olsanskii, G. I., Description of the representations of \(U(p, q)\) with highest weight, Functional Anal. Appl., 14, 32-44 (1980) · Zbl 0439.22019
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