Type $C$ Webs

Abstract

We define a $\mathbb{C}(q)$-linear pivotal category $\mathbf{Web}({\mathfrak{sp}}_{2n})$ and prove that it is equivalent to the full subcategory of finite-dimensional representations of $U_q({\mathfrak{sp}}_{2n})$ tensor-generated by the fundamental representations. This answers the type $C$ case of the main open problem from Kuperberg's 1996 paper "Spiders for rank 2 Lie algebras" (arXiv:q-alg/9712003).

45 pages, many diagrams (some in color)