Explicit generalized Pieri maps

The purpose of this paper is to describe explicitly in a characteristic-free setting certain maps between skew Weyl modules for the general linear group. As an application, we indicate briefly how our generalized Pieri maps are utilized to obtain new results concerning nonzero homomorphisms between certain skew Weyl modules over fields of positive characteristics. In particular, we obtain a new proof of the special case of the Carter-Payne theorem considered in this paper.