On certain identities between Fourier transforms of weighted orbital integrals on infinitesimal symmetric spaces of Guo-Jacquet

TL;DR

This paper establishes identities between Fourier transforms of weighted orbital integrals on local symmetric spaces, aiding the comparison of infinitesimal Guo-Jacquet trace formulae.

Contribution

It proves new relations between Fourier transforms of orbital integrals on symmetric spaces, advancing the understanding of trace formula comparisons.

Findings

Relations between Fourier transforms of orbital integrals are established.

Results facilitate noninvariant comparison of trace formulae.

Contributes to the theory of symmetric spaces and trace formulas.

Abstract

In an infinitesimal variant of Guo-Jacquet trace formulae, the regular semi-simple terms are expressed as noninvariant weighted orbital integrals on two global infinitesimal symmetric spaces. We prove some relations between the Fourier transforms of invariant weighted orbital integrals on the corresponding local infinitesimal symmetric spaces. These relations should be useful in the noninvariant comparison of the infinitesimal variant of Guo-Jacquet trace formulae.