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arXiv · 2607.13252

Type $B$ Webs

Elijah Bodish·Ben Elias·David E. V. Rose
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Abstract

We solve the type $B$ case of the main open problem from Kuperberg's 1996 paper "Spiders for rank 2 Lie algebras." That is, we define a $\mathbb{C}(q)$-linear pivotal category $\mathbf{Web}(\mathfrak{so}_{2n+1})$ and prove that it is equivalent to the full subcategory of finite-dimensional representations of $U_q(\mathfrak{so}_{2n+1})$ tensor-generated by the fundamental representations. A consequence of our main result is an explicit construction of braid group symmetries for nonclassical finite-dimensional representations of the $\iota$quantum group ${U}^{\iota}_{-q^2}(\mathfrak{so}_m)$, which may be of independent interest.

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Elijah Bodish, Ben Elias, David E. V. Rose. 2026-07-14. Type $B$ Webs. https://arxiv.org/abs/2607.13252

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