Workshop on Representation Theory and Geometry

In 1997, Kuperberg gave a generators-and-relations presentation of the monoidal category Fund, whose objects are tensor products of fundamental representations, for all rank 2 lie algebras. The general case has been an open problem since. It was solved in type A in 2014 by Cautis-Kamnitzer-Morrison, and this talk will be about the solution in type C, which is recent work of Bodish-Elias-Rose-Tatham. More importantly, we introduce a basis of our category, analogous to the basis constructed in type A by Elias in 2016. One of the goals of this talk is to explain the philosophy of plethysm patterns and their associated light ladders bases.