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On the algebraic construction and classification of Harish-Chandra modules.

Let G be a connected real semisimple Lie group. In this article a functor is defined which assigns to each irreducible finite dimensional representation of a Cartan subgroup of G a Harish-Chandra module for G. This functor is described by an explicit construction of modules and a sufficient condition is given for the image module to be irreducible. In the case when G is a linear group, this functor is used to exhibit all irreducible Harish-Chandra modules of G.