Harish-Chandra transform explained

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 .

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

f ^{P(m)} = a ^{-\rho} \int _{Nf(nm)dn}

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