\magnification=1200
\hsize=4in
\overfullrule=0pt
\input amssym
%\def\frac#1 #2 {{#1\over #2}}
\def\emph#1{{\it #1}}
\def\em{\it}
\nopagenumbers
\noindent
%
%
{\bf Daniel Kane and Steven Sivek}
%
%
\medskip
\noindent
%
%
{\bf On the ${\cal S}_{n}$-Modules Generated by Partitions of a Given Shape}
%
%
\vskip 5mm
\noindent
%
%
%
%
Given a Young diagram $\lambda$ and the set $H^{\lambda}$ of
partitions of $\{1,2,\dots$, $|\lambda|\}$ of shape $\lambda$, we analyze
a particular ${\cal S}_{|\lambda|}$-module homomorphism
${\Bbb Q}H^{\lambda}\to{\Bbb Q}H^{\lambda'}$ to show that
${\Bbb Q}H^{\lambda}$ is a submodule of ${\Bbb Q}H^{\lambda'}$
whenever $\lambda$ is a hook $(n,1,1,\dots,1)$ with $m$ rows, $n\geq
m$, or any diagram with two rows.



\bye

.