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Mathfrak::''k''    ''V''::action    Algebra::''g''    Group::editor    ''k''::''n''    ''v''::theory

In mathematics, more specifically in the representation theory of reductive Lie groups, a <math>(\mathfrak{g},K)</math>-module is an algebraic object, first introduced by Harish-Chandra,<ref>Page 73 of {{#invoke:Footnotes|harvard_citation_no_bracket}}</ref> 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 <math>(\mathfrak{g},K)</math>-modules, where <math>\mathfrak{g}</math> is the Lie algebra of G and K is a maximal compact subgroup of G.<ref>Page 12 of {{#invoke:Footnotes|harvard_citation_no_bracket}}</ref>


(g,K)-module sections
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