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arXiv · 2506.09729

Affine web of type Q

Linliang Song·Xingyu Wang
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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 $Q$. .

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Linliang Song, Xingyu Wang. 2025-06-11. Affine web of type Q. https://arxiv.org/abs/2506.09729

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