TITLE: Simple modules for $U_q(\mathfrak{sl}_n)$ at roots of unity
QUESTION [12 upvotes]: Can anyone point me to a classification/construction of the irreducibles for $U_q(\mathfrak{sl}_n)$, or the associated small quantum groups, when the parameter $q$ is a root of unity and $n>2$?  Neither Jantzen or Lusztig's quantum group books seem to help.
Edit: perhaps the best way to clarify what I mean when I refer to the `small quantum group' is to give the definition: take the $\mathbb{C}$-algebra (other fields will do) generated by (for $n=3$) $E_1, E_2, F_1, F_2, K_1, K_2$ subject to the following relations.
$$ E_1^2 E_2 - [2] E_1E_2E_1 + E_2 E_1^2 =0 $$
$$ E_2^2 E_1 - [2] E_2E_1E_2 + E_1 E_2^2 =0 $$
and the same relations on the $F$s, where $[2]$ is the quantum integer $q+q^{-1}$
$$ [E_i, F_j] = \delta_{ij} (K_i-K_i^{-1})/(q-q^{-1}) $$
$$ K_i E_j K_i^{-1} = q^{a_{ij}} E_j $$
$$ K_i F_j K_i^{-1} = q^{-a_{ij}} F_j $$
where $[a_{ij}]$ is the Cartan matrix for $\mathfrak{sl}_3$.
$$E_i^N = F_i^N = 0, K_i^N=1$$
and also define $E_{1+2} = qE_2E_1 - E_1E_2$ and $F_{1+2}$ similarly and impose $E_{1+2}^N=F_{1+2}=0$.  I'm convinced this last is necessary for the algebra to be finite-dimensional, though I have seen papers omitting it --- the small quantum group above should be a finite dimensional Hopf algebra with dimension $N^8$, with a PBW basis described by Lusztig.  $q$ is a primitive $N$th root of unity in the field used.

REPLY [5 votes]: I have tracked down some results on explicit classifications of simple modules for $u_q(\mathfrak{sl}_3)$.  The general picture is that the simple modules are bigraded by the root lattice and look like towers of concentric hexagons.
For the benefit of anyone else interested, there is a long series of papers by Dobrev:
Multiplet classification of highest weight modules over quantum universal enveloping algebras: the Uq(SL(3,C)) example in Groups St Andrews 1989 vol 1 LMS LNM #159
Representations of Quantum Groups, Symmetries in Science V (Lochau 1990), 93–135, Plenum Press, NY, 1991.
A chapter from Lecture Notes in Physics, 1990, Volume 370, here
Dobrev-Truini Irregular Uq(sl(3)) representations at roots of unity via Gel’fand–(Weyl)–Zetlin basis
Dobrev-Truini Polynomial realization of the Uq(sl(3)) Gel’fand–(Weyl)–Zetlin basis
MR1182163, MR1191199, 
...and many others.
also there is a paper by
Abdesselam, Arnaudon, Chakrabarti
and a discussion of dimensions by Pereira here
Some of the relevant material is hard to find and/or requires paying large sums of money to publishing corporations.