In mathematical representation theory, the Eisenstein integral is an integral introduced by Harish-Chandra[1] in the representation theory of semisimple Lie groups, analogous to Eisenstein series in the theory of automorphic forms.
Harish-Chandra used Eisenstein integrals to decompose the regular representation of a semisimple Lie group into representations induced from parabolic subgroups.
[2] Trombi gave a survey of Harish-Chandra's work on this.
[3] Harish-Chandra[4] defined the Eisenstein integral by where: