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An intrinsic analysis of unitarizable highest weight modules. (English) Zbl 0725.17009
The authors analyze the structure of unitarizable highest weight modules for a real form of a complex simple Lie algebra. This analysis enables to avoid some case by case considerations in the proofs of the unitarizability criterion due to Enright-Howe-Wallach [T. Enright et al., Prog. Math. 40, 97–143 (1983; Zbl 0535.22012)] and H. P. Jakobsen [J. Funct. Anal. 52, 385–412 (1983; Zbl 0517.22014)] of 1983. They also establish a strong connection between unitarity and invariant theory in this setting.

MSC:
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
17B20 Simple, semisimple, reductive (super)algebras
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