Quantum affine Lie algebras and Gl(n) over non-Archimedean local fields

We will discus the relationship between the representation theory of quantum affine Lie algebras and that of groups of matrices over non-Archimedean local fields, such as the p-adic numbers. In particular, we will address the question of when the tensor of two simple representations of a quantum affine lie algebra is simple and the corresponding question of when the parabolic induction of two simple representations of p-adic matrices is simple. We will focus on the case of affine sl(2) and p-adic Gl(n), where the relationship between the categories is well-understood.