  In this paper, we explore the use of path idempotents for the Hecke algebra
of type $A$ at roots of unity. For $q$ a primitive $\ell$-th root of unity we
obain a non-unital imbedding of (a quotient of) the group algebra of $S_m$ into
(a quotient of) the Hecke algebra $H_n(q)$ for certain $m$ and $n$. From this
we recover certain instances of irreducibility criteria of Dipper, James, and
Mathas, and we derive estimates on the decomposition numbers for the Hecke
algebra at roots of unity. The bounds are easily computed, provide a good
geometric picture of the pairs of diagrams $\lambda$, $\mu$ for which the
decomposition number $d_{\lambda, \mu}$ is non-zero, and also appers to be a
useful adjunct to the exact computation of the decomposition numbers.
