Produced Representations of Lie Algebras and Harish-Chandra Modules

Michael J. Heumos
1987 Transactions of the American Mathematical Society  
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 f·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 applica· tion describes a
more » ... etting where the Zuckerman functors and production from a subalgebra commute.
doi:10.2307/2000855 fatcat:e64fjepzifgj5j72azlue33opq