Canonical bases of the oriented skein category

Abstract

We develop a bar involution and canonical basis for every morphism space of the oriented skein category through a diagrammatic approach. In particular, our construction gives rise to Kazhdan-Lusztig type bases on quantized walled Brauer algebras.

arXiv commentv1. 27 pages; v2. added reference, modified introduction; v3. we extend the constructions from the algebra level to all morphism spaces of the oriented category