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 integrable highest weight modules of a bigger quantum group. As a result, based on the positivity of the canonical bases of the integrable highest weight modules due to Lusztig, we prove that the canonical bases of the tensor products have the positivity.

Final version. Published in International Mathematics Research Notices (2025)