Les formules des traces relatives de Jacquet-Rallis grossi\`eres

TL;DR

This paper proves coarse relative trace formulas for linear and unitary groups, introducing new truncation operators and using descent techniques to relate spectral and geometric distributions.

Contribution

It establishes the coarse relative trace formulas of Jacquet-Rallis for linear and unitary groups, with new truncation operators and geometric decompositions via descent methods.

Findings

Spectral distributions are expressed as sums of spectral components.

Geometric distributions are derived from descent to tangent spaces.

New truncation operators are introduced and analyzed.

Abstract

We establish the coarse relative trace formulae of Jacquet-Rallis for linear and unitary groups. Both formulae are of the form: a sum of spectral distributions equals a sum of geometric distributions. In order to obtain the spectral decompositions we introduce new truncation operators and we investigate their properties. On the geometric side, by means of the Cayley transform, the decompositions are derived from a procedure of descent to the tangent spaces for which the formulae are known thanks to our previous work.