Irreducible completely pointed modules of quantum groups of type A

We give a classification of all irreducible completely pointed Uq(sln+1) modules over a characteristic zero field in which q is not a root of unity. This generalizes the classification result of Benkart, Britten and Lemire in the non-quantum case. We also show that any infinite-dimensional irreducible completely pointed Uq(sln+1) can be obtained from some irreducible completely pointed module over the quantized Weyl algebra An+1q.