Young diagrams and simple constituents of the Specht modules

Abstract

We discuss the simple constituents of Specht module $S^{\lambda}$ for the symmetric group $S_n$ defined over the field of $p$ elements. We firstly give an easier proof to the result in [6] which asserts that there exists a simple constituent of $S^{\lambda}$ with the shape of ``a branch'' of $\lambda$ (Theorem 3.3), and secondly give a sufficient condition for $\lambda$ to have a particular type branch as a constituent (Proposition 3.4).