What is "-module"

In mathematics, more specifically in the representation theory of reductive Lie groups, a (g, K)-module is an algebraic object, first introduced by Harish-Chandra, used to deal with continuous infinite-dimensional representations using algebraic techniques. Harish-Chandra showed that the study of irreducible unitary representations of a real reductive Lie group, G, could be reduced to the study of irreducible (g, K)-modules, where g is the Lie algebra of G and K is a maximal compact subgroup of G.