Harish-Chandra transform

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In mathematical representation theory, the Harish-Chandra transform is a linear map from functions on a reductive Lie group to functions on a parabolic subgroup. It was introduced by Harish-Chandra (1958, p.595).

The Harish-Chandra transform fP of a function f on the group G is given by

where P = MAN is the Langlands decomposition of a parabolic subgroup.