Orbital Integrals on Forms of SL(3), II

Abstract

In the paper [6] we described in a precise fashion the notion of transfer of orbital integrals from a reductive group over a local field to an endoscopic group. We did not, however, prove the existence of the transfer. This remains, indeed, an unsolved problem, although in [7] we have reduced it to a local problem at the identity. In the present paper we solve this local problem for two special cases, the group SL(3), which is not so interesting, and the group SU(3), and then conclude that transfer exists for any group of type A2. The methods are those of [4], and are based on techniques of Igusa for the study of the asymptotic behavior of integrals on p-adic manifolds. (As observed in [7], the existence of the transfer over archimedean fields is a result of earlier work by Shelstad.)