  In a previous paper, the authors studied the radical filtration of a Weyl
module $\Delta_\zeta(\lambda)$ for quantum enveloping algebras
$U_\zeta(\overset\circ{\mathfrak g})$ associated to a finite dimensional
complex semisimple Lie algebra $\overset\circ{\mathfrak g}$. There
$\zeta^2=\sqrt[e]{1}$ and $\lambda$ was, initially, required to be $e$-regular.
Some additional restrictions on $e$ were required---e.g., $e>h$, the Coxeter
number, and $e$ odd.
  Translation to a facet gave an explicit semisimple series for all quantum
Weyl modules with singular, as well as regular, weights. That is, the sections
of the filtration are explicit semisimple modules with computable
multiplicities of irreducible constituents. However, in the singular case, the
filtration conceivably might not be the radical filtration. This paper shows
how a similar semisimple series result can be obtained for all positive
integers $e$ in case $\overset\circ{\mathfrak g}$ has type $A$, and for all
positive integes $e\geq 3$ in type $D$. One application describes semisimple
series (with computable multiplicities) on $q$-Specht modules. We also discuss
an analogue for Weyl modules for classical Schur algebras and Specht modules
for symmetric group algebras in positive characteristic $p$. Here we assume the
James Conjecture and a version of the Bipartite Conjecture.
