An -cohomology construction of unitary highest weight modules for

Author:
Lisa A. Mantini

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

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Abstract: In this paper a geometric construction is given of all unitary highest weight modules of . The construction is based on the unitary model of the 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 , and the construction is implemented via an integral transform analogous to the Penrose transform of mathematical physics.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1991-1020992-9

Keywords:
Semisimple Lie groups,
unitary representations,
highest weight modules,
metaplectic representation,
integral transform

Article copyright:
© Copyright 1991
American Mathematical Society