Eisenstein integral

In mathematical representation theory, the Eisenstein integral is an integral introduced by Harish-Chandra (1970, 1972) in the representation theory of semisimple Lie groups, analogous to Eisenstein series in the theory of automorphic forms. Harish-Chandra (1975, 1976a, 1976b) used Eisenstein integrals to decompose the regular representation of a semisimple Lie group into representations induced from parabolic subgroups. Trombi (1989) gave a survey of Harish-Chandra's work on this.

Harish-Chandra (1970, section 10) defined the Eisenstein integral by

where:

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