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

MSC:
22E46 Semisimple Lie groups and their representations
22E47 Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.)
17B35 Universal enveloping (super)algebras
32M15 Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects)
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References:
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[2] Enright, T.J., Parthasarathy, R.: A proof of a conjecture of Kashiwara and Vergne. Preprint, 1980 · Zbl 0492.22012
[3] Humphreys, J.E.: Introduction to Lie algebras and representation theory Berlin, Heidelberg, New York: Springer 1972 · Zbl 0254.17004
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[5] Jakobsen, H.P.: On singular holomorphic representations. Invent Math.62, 67-78 (1980) · Zbl 0466.22016 · doi:10.1007/BF01391663
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[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
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