Webs of Type P

TL;DR

This paper introduces type P web supercategories as diagrammatic models for the monoidal supercategory generated by symmetric powers of the natural module and their duals for Lie superalgebra type P, providing bases and structural insights.

Contribution

It defines and studies type P web supercategories, establishing their structure and their role as combinatorial models for specific Lie superalgebra representations.

Findings

Provided diagrammatic bases for morphism spaces.

Established supercategories as models for symmetric powers of Lie superalgebra modules.

Analyzed the structure of type P web supercategories.

Abstract

This paper introduces type P web supercategories. They are defined as diagrammatic monoidal $k$-linear supercategories via generators and relations. We study the structure of these categories and provide diagrammatic bases for their morphism spaces. We also prove these supercategories provide combinatorial models for the monoidal supercategory generated by the symmetric powers of the natural module and their duals for the Lie superalgebra of type P.