Type $C$ Webs Article Swipe
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Business
Elijah Bodish
,
Ben Elias
,
David E. V. Rose
,
Logan Tatham
·
YOU?
·
· 2021
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2103.14997
· OA: W4394653384
YOU?
·
· 2021
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2103.14997
· OA: W4394653384
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).
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