Webs of type Q

TL;DR

This paper introduces web supercategories of type Q, demonstrating their structure and symmetric braiding, and showing they serve as combinatorial models for supersymmetric tensor powers in Lie superalgebra of type Q.

Contribution

It defines and analyzes web supercategories of type Q, establishing their structure and their role as models for supersymmetric tensor powers in Lie superalgebras.

Findings

Web supercategories of type Q have symmetric braiding.

They provide combinatorial models for supersymmetric tensor powers.

The categories are diagrammatically defined monoidal supercategories.

Abstract

We introduce web supercategories of type Q. We describe the structure of these categories and show they have a symmetric braiding. The main result of the paper shows these diagrammatically defined monoidal supercategories provide combinatorial models for the monoidal supercategories generated by the supersymmetric tensor powers of the natural supermodule for the Lie superalgebra of type Q.