Young's seminormal basis vectors and their denominators

TL;DR

This paper investigates Young's seminormal basis vectors for dual Specht modules of the symmetric group, focusing on their denominators and implications for module morphism splitting over localized integers.

Contribution

It provides new insights into the denominators of Young's seminormal basis vectors and their role in the splitting of canonical morphisms in Schur algebra modules.

Findings

Identifies specific basis vectors controlling morphism splitting

Analyzes denominators related to standard tableaux

Connects basis properties to module decomposition

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 $\nu$.