Harish-Chandra module
In mathematics, specifically in the representation theory of Lie groups, a Harish-Chandra module, named after the Indian mathematician and physicist Harish-Chandra, is a representation of a real Lie group, associated to a general representation, with regularity and finiteness conditions. When the associated representation is a -module, then its Harish-Chandra module is a representation with desirable factorization properties.Definition
Let G be a Lie group and K a compact subgroup of G. If is a representation of G, then the Harish-Chandra module of is the subspace X of V consisting of the K-finite smooth vectors in V. This means that X includes exactly those vectors v such that the map via
is smooth, and the subspace
is finite-dimensional.
