Produced representations of Lie algebras and Harish-Chandra modules

Heumos, Michael J.

doi:10.1090/S0002-9947-1987-0891633-5

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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