Endoscopic transfer between eigenvarieties for definite unitary groups

TL;DR

This paper develops a p-adic interpolation of endoscopic transfer for definite unitary groups, constructing a rigid analytic map between eigenvarieties that extends classical transfer to finite slope automorphic forms.

Contribution

It introduces a novel rigid analytic map between eigenvarieties that generalizes endoscopic transfer to finite slope p-adic automorphic forms for definite unitary groups.

Findings

Constructed a rigid analytic map between eigenvarieties.

Interpolates classical endoscopic transfer at classical points.

Extends transfer to finite slope p-adic automorphic forms.

Abstract

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