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What (who) is (g,K)-module - definition
(g,K)-module
ALGEBRAIC OBJECT
In mathematics, more specifically in the representation theory of reductive Lie groups, a (\mathfrak{g},K)-module is an algebraic object, first introduced by Harish-Chandra,Page 73 of 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 (\mathfrak{g},K)-modules, where \mathfrak{g} is the Lie algebra of G and K is a maximal compact subgroup of G.
Module (mathematics)
GENERALIZATION OF VECTOR SPACE, WITH SCALARS IN A RING INSTEAD OF A FIELD
Module (algebra); Submodule; Module theory; Submodules; R-module; Module over a ring; Left module; Module Theory; Unital module; Module (ring theory); Right module; Left-module; Module mathematics; Ring action; Z-module; ℤ-module
In mathematics, a module is a generalization of the notion of vector space in which the field of scalars is replaced by a ring. The concept of module generalizes also the notion of abelian group, since the abelian groups are exactly the modules over the ring of integers.
Dualizing module
In abstract algebra, a dualizing module, also called a canonical module, is a module over a commutative ring that is analogous to the canonical bundle of a smooth variety. It is used in Grothendieck local duality.
Wikipedia
(g,K)-module
In mathematics, more specifically in the representation theory of reductive Lie groups, a (\mathfrak{g},K)-module is an algebraic object, first introduced by Harish-Chandra,Page 73 of 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 (\mathfrak{g},K)-modules, where \mathfrak{g} is the Lie algebra of G and K is a maximal compact subgroup of G.
