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In his seminal 1996 paper, Kuperberg gives presentations for the categories of finite-dimensional representations of quantum groups associated to rank 2 simple complex Lie algebras (as braided pivotal categories). Such presentations underly constructions of invariants in low-dimensional topology; in particular, they serve as a "foundation" for various link homology theories. Kuperberg also poses the following problem: to find analogous descriptions of these categories for quantum groups of higher rank. In 2012, Cautis-Kamnitzer-Morrison solved this problem in type A using skew Howe duality, a technique that does not extend (at least in a straightforward way) to give a solution in other types.

In this talk, we will present a solution to Kuperberg's problem in type C. Our proof combines results on pivotal categories and quantum group representations with diagrammatic/topological analogues of theorems concerning reduced expressions in the symmetric group. Time permitting, we'll discuss some future directions. This work is joint with Bodish, Elias, and Tatham (on the arXiv soon!) and builds on previous work with Tatham (https://arxiv.org/abs/2006.02491).

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