Fourier Transforms of Nilpotent, Coadjoint Orbits for GL(n,R)

Abstract

The main result of this paper is an explicit formula for the Fourier transform of the canonical measure on a nilpotent coadjoint orbit for GL(n,R). This paper also includes some results on limit formulas for reductive Lie groups including new proofs of classical limit formulas of Rao and Harish-Chandra.