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

 

Produced representations of Lie algebras and Harish-Chandra modules


Author: Michael J. Heumos
Journal: Trans. Amer. Math. Soc. 302 (1987), 523-534
MSC: Primary 17B10; Secondary 17B20, 22E47
MathSciNet review: 891633
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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

DOI: http://dx.doi.org/10.1090/S0002-9947-1987-0891633-5
PII: S 0002-9947(1987)0891633-5
Article copyright: © Copyright 1987 American Mathematical Society