Canonical bases of tensor products of integrable highest weight modules arising from framed constructions

Abstract: Given a quantum group, we prove that the canonical bases of the tensor products of its integrable highest weight modules can be obtained from the canonical bases of the simple integrable highest modules of a bigger quantum group. As a result, based on the positivity of the canonical bases of the simple integrable highest modules due to Lusztig, we prove that the canonical bases of the tensor products have the positivity.