Positivity and the canonical basis of tensor products of   finite-dimensional irreducible representations of quantum sl(k)
  In a categorification of tensor products of fundamental representations of quantum sl(k) via highest weight categories, the indecomposable tilting modules descend to the canonical basis. Since projective functors map tilting modules to tilting modules, the coefficients of the canonical basis of tensor products of finite dimensional, irreducible representations under the action of the Chevalley generators are positive. 
Joshua Sussan