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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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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.
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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