A Global Trace Formula for Reductive Lie Algebras and the Harish-Chandra Transform on the Space of Characteristic Polynomials

Abstract

In this paper an integral transform between spaces of nonstandard test functions on the affine space of dimension n is constructed. The integral transform satisfies a summation formula of Poisson type, which is derived from an analogue of the Arthur-Selberg trace formula for the Lie algebra of n by n matrices.