Webs are certain diagrams used to represent homomorphisms between tensor products of representations for various Lie (super)algebras. These diagrams can be assembled into a monoidal ‘web category’, and typically there is a full functor from the web category into the category of representations of the associated Lie superalgebra. In this talk, I will discuss recent work that deforms web categories by decorating the diagrams with elements of some superalgebra A. These ‘decorated’ webs generalize several constructions that have previously appeared in the literature, including webs for the Lie algebra 𝔤𝔩n(â„‚), the Lie superalgebra đť”®(n). The webs also give a diagrammatic presentation for the so-called Schurification of A.
This work is joint with Jonathan Kujawa, Robert Muth, and Jieru Zhu.
This video was part of the Southeastern Lie Theory Workshop XIII.
