An $L^ 2$-cohomology construction of unitary highest weight modules for $\textrm {U}(p,q)$
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- by Lisa A. Mantini PDF
- Trans. Amer. Math. Soc. 323 (1991), 583-603 Request permission
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.References
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Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 323 (1991), 583-603
- MSC: Primary 22E45; Secondary 32L25, 32M15, 58G05
- DOI: https://doi.org/10.1090/S0002-9947-1991-1020992-9
- MathSciNet review: 1020992