Higher Tensor Product for sl2 and Webster algebras

TL;DR

This paper introduces a simplified, equivalent model for the tensor product of certain 2-representations of rak{sl}_2^+ and Webster algebras, based on inf categorical methods.

Contribution

It constructs a new, simpler tensor product model that encompasses McMillan's minimal model and proves its equivalence to Webster's tensor product category.

Findings

The new model simplifies the tensor product construction.

It contains McMillan's minimal model as a special case.

The model is proven equivalent to Webster's tensor product category.

Abstract

We construct a model for the tensor product of the regular 2-representation of the enveloping algebra of $\mathfrak{sl}_2^+$ with the vector 2-representation, based on the $\infty$-categorical definition of the second author. Our model contains McMillan's minimal one. Our use of an infinite family of generators provides a simpler model that we prove is equivalent to Webster's tensor product category.