Mark Ebert, UCLA

Title: Higher tensor products for sl(2)

Abstract: Webster famously introduced a categorification of tensor products of simple representations for general Kac-Moody algebras and used them to categorify the Reshetikhin–Turaev invariants. While we can categorify tensor products of representations, the ability to define an explicit "higher" tensor product of categorified representations of Kac-Moody algebra has still not been fully realized.
 
Rouquier defined a general tensor 2-product operation for 2-representations of Kac-Moody algebras in an infinity-categorical setting, and conjectures that these agree with Webster's 2-representations. In joint work with Raphael Rouquier, we construct a model for the tensor product of the regular 2-representation of sl_2^+ with the vector 2-representation and show that it agrees with the 2-representation of Webster, partially proving Rouquier's conjecture. Our model has the same starting point as that of the minimal model of McMillan, but our use of an infinite family of generators makes our model significantly simpler, which we use to prove the equivalence.TBA