Endoscopic transfer between eigenvarieties for definite unitary groups

Abstract

In this paper, we extend the endoscopic transfer of definite unitary group U(n), which sends a pair of automorphic forms of U(n {1}), U(n {2}) to an automorphic form of U(n {1} + n {2}), to finite slope p-adic automorphic forms for definite unitary groups by constructing a rigid analytic map between eigenvarieties E n {1} × E {n {2}} → E {(n {1} + n {2})}, which at classical points interpolates endoscopic transfer map.