p-adic monodromy of the ordinary locus of Picard moduli scheme

Let E be an imaginary quadratic number field, p a rational prime splitting in [special characters omitted] and let m, n be distinct natural numbers. The naive p-adic monodromy of the ordinary locus of the good reduction of a Shimura variety of U(m, n) type over [special characters omitted] is a subgroup of GLm([special characters omitted]) × GLn([special characters omitted]). In this paper, we prove that for any point in the basic locus of the moduli space, the local monodromy is an open subgroup of GL m([special characters omitted]) × GLn([special characters omitted]). From this local information, the global p-adic monodromy is shown to be as big as possible, i.e. GLm([special characters omitted]) × GLn([special characters omitted])