Web bases for the Lie superalgebra gl(1|1)

Queffelec--Sartori and Tubbenhauer--Vaz--Wedrich give a diagrammatic web category via generators and relations to describe the subcategory of Rep(gl(m|n)) generated by tensor products of exterior powers of the defining representation. We construct the first explicit bases for homomorphism spaces in the web category for gl(1|1), giving an alternative diagrammatic presentation of this web category, and explore connections to the combinatorics of planar networks. Our basis comes equipped with an algorithm to decompose any web into a linear combination of basis webs, giving an effective way to compute in the gl(1|1)-skein theory.