Skew Pieri algebras of the general linear group

Abstract

Let V be an irreducible polynomial representation of the general linear group GLn=GLn(C) and let α1, …, αq be nonnegative integers less than or equal to n. We call a description of the irreducible decomposition of the tensor product V⊗Λα1(Cn)⊗⋯⊗Λαq(Cn) an iterated skew Pieri rule for GLn. In this paper, we define a family of complex algebras whose structure encodes an iterated skew Pieri rule for GLn, and we call these algebras iterated skew Pieri algebras. Our main goal is to construct a basis for each of these algebras thereby giving explicit highest weight vectors in the above tensor product.