Ap-ADIC HERMITIAN MAASS LIFT

Abstract

AbstractForK, an imaginary quadratic field with discriminant −DK, and associated quadratic Galois character χK, Kojima, Gritsenko and Krieg studied a Hermitian Maass lift of elliptic modular cusp forms of levelDKand nebentypus χKvia Hermitian Jacobi forms to Hermitian modular forms of level one for the unitary groupU(2, 2) split overK. We generalize this (under certain conditions onKandp) to the case ofp-oldforms of levelpDKand character χK. To do this, we define an appropriate Hermitian Maass space for general level and prove that it is isomorphic to the space of special Hermitian Jacobi forms. We then show how to adapt this construction to lift a Hida family of modular forms to ap-adic analytic family of automorphic forms in the Maass space of levelp.