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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

An $ L\sp 2$-cohomology construction of unitary highest weight modules for $ {\rm U}(p,q)$


Author: Lisa A. Mantini
Journal: Trans. Amer. Math. Soc. 323 (1991), 583-603
MSC: Primary 22E45; Secondary 32L25, 32M15, 58G05
MathSciNet review: 1020992
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Abstract: In this paper a geometric construction is given of all unitary highest weight modules of $ G = \operatorname{U} (p,q)$. The construction is based on the unitary model of the $ k$th tensor power of the metaplectic representation in a Bargmann-Segal-Fock space of square-integrable differential forms. The representations are constructed as holomorphic sections of certain vector bundles over $ G/K$, and the construction is implemented via an integral transform analogous to the Penrose transform of mathematical physics.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1991-1020992-9
PII: S 0002-9947(1991)1020992-9
Keywords: Semisimple Lie groups, unitary representations, highest weight modules, metaplectic representation, integral transform
Article copyright: © Copyright 1991 American Mathematical Society