  In this paper we give an alternate combinatorial description of the
"$(\ell,0)$-JM partitions" (see \cite{F}) that are also $\ell$-regular. Our
main theorem is the equivalence of our combinatoric and the one introduced by
James and Mathas (\cite{JM}). The condition of being an $(\ell,0)$-JM partition
is fundamentally related to the hook lengths of the partition. The
representation-theoretic significance of their combinatoric on an
$\ell$-regular partition is that it indicates the irreducibility of the
corresponding specialized Specht module over the finite Hecke algebra (see
\cite{JM}). We use our result to find a generating series which counts the
number of such partitions, with respect to the statistic of a partition's first
part. We then apply our description of these partitions to the crystal graph
$B(\Lambda_0)$ of the basic representation of $\hat{\mathfrak{sl}_{\ell}}$,
whose nodes are labeled by $\ell$-regular partitions. Here we give a fairly
simple crystal-theoretic rule which generates all $\ell$-regular $(\ell,0)$-JM
partitions in the graph $B(\Lambda_0)$. Finally, we mention how our
construction can be generalized to recent results of M. Fayers (see \cite{F})
and S. Lyle (see \cite{L}) to count the total number of (not necessarily
$\ell$-regular) Specht modules which stay irreducible at a primitive $\ell$th
root of unity (for $\ell >2$).
