I will talk about work in progress concerning the ring structure of certain endomorphism algebras of tensor products of modules for quantum sl(2). I will focus on the case where the quantum parameter is allowed to be a root of unity.

The main result of the work so far is the existence (under certain nice conditions) of a surjection from the group algebra of the braid group to the endomorphism algebra of the Weyl module with highest weight 2 tensored with itself any number of times.