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The last possible place of unitarity for certain highest weight modules. (English) Zbl 0478.22007

MSC:
22E46Semisimple Lie groups and their representations
22E47Representations of Lie and real algebraic groups: algebraic methods
17B35Universal enveloping Lie (super)algebras
32M15Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (analytic spaces)
References:
[1]Dixmier, J.: Algebrès enveloppantes. Paris: Gauthier-Villars 1972
[2]Enright, T.J., Parthasarathy, R.: A proof of a conjecture of Kashiwara and Vergne. Preprint, 1980
[3]Humphreys, J.E.: Introduction to Lie algebras and representation theory Berlin, Heidelberg, New York: Springer 1972
[4]Jakobsen, H.P., Vergne, M.: Restrictions and expansions of holomorphic representations. J. Functional Analysis34, 29-53 (1979) · Zbl 0433.22011 · doi:10.1016/0022-1236(79)90023-5
[5]Jakobsen, H.P.: On singular holomorphic representations. Invent Math.62, 67-78 (1980) · Zbl 0466.22016 · doi:10.1007/BF01391663
[6]Kashiwara, M., Vergne, M.: On the Segal-Shale-Weil repiesentation and harmonic polyncmials. Invent. Math.44, 1-47 (1978) · Zbl 0375.22009 · doi:10.1007/BF01389900
[7]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 · doi:10.1007/BF02392042
[8]Shapovalov, N.N.: On a bilinar form on the universal enveloping algebra of a complex semi-simple Lie algebra. Functional Analysis Appl.6, 307-312 (1972) · Zbl 0283.17001 · doi:10.1007/BF01077650