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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality 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 1.43.

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Produced representations of Lie algebras and Harish-Chandra modules
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by Michael J. Heumos PDF
Trans. Amer. Math. Soc. 302 (1987), 523-534 Request permission

Abstract:

The comultiplication of the universal enveloping algebra of a Lie algebra is used to give modules produced from a subalgebra, an additional compatible structure of a module over an algebra of formal power series. When only the $\mathfrak {k}$-finite elements of this algebra act on a module, conditions are given that insure that it is the Harish-Chandra module of a produced module. The results are then applied to Zuckerman derived functor modules for reductive Lie algebras. The main application describes a setting where the Zuckerman functors and production from a subalgebra commute.
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Additional Information
  • © Copyright 1987 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 302 (1987), 523-534
  • MSC: Primary 17B10; Secondary 17B20, 22E47
  • DOI: https://doi.org/10.1090/S0002-9947-1987-0891633-5
  • MathSciNet review: 891633