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 ${\displaystyle ({\mathfrak {g}},K)}$-module, then its Harish-Chandra module is a representation with desirable factorization properties.