The characters of supercuspidal representations as weighted orbital integrals
The author shows how the character of a supercuspidal representation of a reductive Lie group over a non-archimedean local field of characteristic zero is given, up to a factor, as an orbital integral of a matrix coefficient of the representation. The orbital integral is of the type that arise in the author's general version of the Selberg trace formula. The proof is an ingenious deduction using the geometry of reductive groups from an expression of Harish-Chandra's giving the character in terms of an integral of a matrix coefficient.
scientific article; zbMATH DE number 4063418