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Type $C$ Webs (2103.14997v1)
Published 27 Mar 2021 in math.RT and math.QA
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).