Affine web of type Q

TL;DR

This paper introduces an affine web supercategory of type Q, providing a diagrammatic model with integral bases for Hom-spaces, extending the web category framework to affine and super settings.

Contribution

It constructs a new affine web supercategory of type Q, generalizing previous web categories and establishing a combinatorial model for superfunctors of Lie superalgebras of type Q.

Findings

Diagrammatic integral bases for Hom-spaces

Construction of the affine web supercategory of type Q

Model for endosuperfunctors of Lie superalgebras of type Q

Abstract

We introduce a new diagrammatic $\Bbbk$-linear monoidal supercategory $QWeb^\bullet$, the affine web supercategory of type $Q$, where $\Bbbk$ is a commutative ring of characteristic not two. This category is the affinization of the web category of type $Q$, originally introduced by Brown and Kujawa. It serves as the type $Q$ analog of the affine web category introduced by Davidson, Kujawa, Muth and Zhu, and independently by Wang and one of the authors. We obtain diagrammatic integral bases for the Hom-spaces of this category. We show that $QWeb^\bullet$ provides a combinatorial model for a natural monoidal supercategory of endosuperfunctors for Lie superalgebras of type $Q$. .