Affine webs of type Q

Abstract

We introduce a new diagrammatic \(\Bbbk \)-linear monoidal supercategory , the affine web supercategory of type Q, where \(\Bbbk \) is a commutative ring in which 2 is invertible. This category is the affinization of the web supercategory of type Q, originally introduced by Brown and Kujawa. It serves as the type Q analog of the affine web category (of type A) introduced by Davidson, Kujawa, Muth, and independently by Wang and the first named author. We obtain diagrammatic integral bases for the Hom-spaces of this category. We show that provides a combinatorial model for a natural monoidal supercategory of endosuperfunctors for Lie superalgebras of type Q.