  Let $\mfp(d)$ be a standard parabolic subalgebra of $\mfsl_{n+1}(K)$ and
$\mfu$ be the corresponding nilradical defined over an algebraically closed
field $K$ of characteristic $p>0$. We construct a finite connected quiver
$Q(d)$, through which we provide a combinatorial characterization of the
centralizer $c_{\mfu}(x(d))$ of the Richardson element $x(d)$. We specifically
focus on the centralizer when the levi factor of $\mfp(d)$ is determined by
either one or two simple roots. This allows us to demonstrate that, under
certain mild restrictions, the saturation rank of $\mfu$ equals the semisimple
rank of the algebraic $K$-group $\SL_{n+1}(K)$.
