Skew Pieri algebras of the general linear group

Abstract

Let V be an irreducible polynomial representation of the general linear group GL(n) = GL(n)(C) and let alpha(1), ... , alpha(q) be nonnegative integers less than or equal to n. We call a description of the irreducible decomposition of the tensor product V circle times Lambda(alpha 1) (C-n) circle times ... circle times Lambda(alpha q)(C-n) an iterated skew Pieri rule for GL(n). In this paper, we define a family of complex algebras whose structure encodes an iterated skew Pieri rule for GL(n), 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. Published by AIP Publishing.