 Let "G" be a Lie group and "K" a compact subgroup of "G".If formula_2 is a representation of "G", then the "Harish-Chandra module" of formula_3 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 formula_4 via

is smooth, and the subspace

is finite-dimensional.