(g,K)-module

In mathematics, more specifically in the representation theory of reductive Lie groups, a ${\displaystyle ({\mathfrak {g}},K)}$-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 ${\displaystyle ({\mathfrak {g}},K)}$-modules, where ${\displaystyle {\mathfrak {g}}}$ is the Lie algebra of G and K is a maximal compact subgroup of G.

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