Irreducibility of Newton strata in Picard modular surfaces and split local Galois representations

Abstract

We show that for a Picard modular form, the existence of companion forms is equivalent to the splitting properties of the associated local Galois representation. This result is obtained by using the computation of the monodromy group and the irreducibility for the closure of the non-ordinary Newton stratum in the special fiber of the Picard modular surface at a split prime.