Pullback Formula for Vector-Valued Hermitian Modular Forms on U_n,n

Using a differential operator which sends a scalar-valued hermitian modular form to the tensor product of two vector-valued hermitian modular forms, under a certain condition, we give the pullback formula for vector-valued hermitian modular forms on any CM field. We also give equivalence conditions for differential operators to have the above properties, which is an extension of Ibukiyama’s result for hermitian modular forms.