Young's seminormal basis vectors and their denominators

Abstract

We study Young’s seminormal basis vectors of the dual Specht modules of the symmetric group, indexed by a certain class of standard tableaux, and their denominators. These vectors include those whose denominators control the splitting of the canonical morphism Δ(λ+μ) → Δ(λ)⊗Δ(μ) over Z(p), where Δ(ν) is the Weyl module of the classical Schur algebra labelled by ν.