Let us consider the quantum group $U_q(\mathfrak{sl}_2)$ (as defined in Kassel's book on quantum groups), for $q$ being a root of unity of order $d$ $\ $ (i.e. $d$ is the smallest integer for which $q^d=1$). If $n$ is the dimension of an irreducible, fin dim rep (over a complex vector space), then it is known that $n$ is bounded by 
$$
e=\{
\begin{array}{c}
d ,& d:odd \\ 
d/2, & d:even
\end{array}
$$
As far as i know, there are indecomposable, non-simple modules of dimension higher than $e$. I have made some small search on the structure of such modules, but i have not found anything substantial apart from [this][1] article, which however refers to the restricted case. So my questions are: 

> 1. Is there some reference on the structure of indecomposable, non-simple modules of quantum groups at roots of unity? 
> 1. How can the limits of such representations at $q\to 1$, be computed? 

I would be interested either on references or on some short -if possible-  description of such modules, mainly for the case of $U_q(\mathfrak{sl}_2)$ and more generally for $U_q(\mathfrak{g})$, where $\mathfrak{g}$ is a fin dim, simple, complex Lie algebra. 

**Related:**

 - https://mathoverflow.net/q/307436/85967
 - https://mathoverflow.net/q/239893/85967


 


  [1]: https://www.jstage.jst.go.jp/article/kyotoms1969/30/2/30_2_335/_pdf