Young's seminormal form and simple modules for $S_n$ in characteristic $p$

TL;DR

This paper provides a new realization of Specht modules for symmetric groups in characteristic p using Jucys-Murphy elements, leading to insights into simple modules via reductions modulo p.

Contribution

It introduces a novel approach to constructing simple modules for $S_n$ in characteristic p through induced modules from Jucys-Murphy elements.

Findings

Realization of Specht modules as induced modules from Jucys-Murphy subalgebra

Simple modules generated by reductions of Jucys-Murphy idempotents

Connection between integral and modular representations of $S_n$

Abstract

We realize the integral Specht modules for the symmetric group $S_n$ as induced modules from the subalgebra of the group algebra generated by the Jucys-Murphy elements. We deduce from this that the simple modules for $FS_n$ are generated by reductions modulo $p$ of the corresponding Jucys-Murphy idempotents.