An infinitesimal variant of the Guo-Jacquet trace formula. I: The case of $({\mathrm{GL}}_{2n,D},{\mathrm{GL}}_{n,D}\times {\mathrm{GL}}_{n,D})$

Abstract

We establish an infinitesimal variant of Guo-Jacquet trace formula for the case of $(G{L}_{2n,D},G{L}_{n,D}\times G{L}_{n,D})$. It is a kind of Poisson summation formula obtained by an analogue of Arthur's truncation process. It consists in the equality of the sums of two types of distributions which are non-equivariant in general: one type is associated to rational points in the categorical quotient, while the other type is the Fourier transform of the first type. For regular semi-simple points in the categorical quotient, we obtain weighted orbital integrals.