TITLE: semisimplicity of braid reps?
QUESTION [5 upvotes]: Here's something I really feel I should know, but do not: 
Let $q$ be some sufficiently nice complex number (just pretend we're working over $\mathbb Q(q)$, for example), and $V$ some simple representation of $U_q(\mathfrak g)$. Then you have the usual representation of the braid group $B_n$ on $V^{\otimes n}$. The question is: is this representation semisimple? 
I haven't been able to find a direct reference to the problem, but it really sounds like it should be known so I thought I'd check here.

REPLY [3 votes]: A complete analysis of this is given in the paper by Orellana-Ram. Actually, they consider the action of the affine braid group on $M\otimes V^{\otimes n}$, but you can recover your case by taking $M$ to be the trivial module. I believe that this is is a semisimple representation (assuming you mean $V$ to be finite dimensional), but in any case it is all spelled out in the paper above.