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 $\Delta (\lambda +\mu )\to \Delta (\lambda )\otimes \Delta (\mu )$ over ${\mathbb{Z}}_{(p)}$, where $\Delta (\nu )$ is the Weyl module of the classical Schur algebra labelled by $\nu$.