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Type $C$ Webs

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arxiv 2103.14997 v1 pith:2QROHTK2 submitted 2021-03-27 math.RT math.QA

Elijah Bodish , Ben Elias , David E. V. Rose , Logan Tatham This is my paper · ORCID
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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).

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Type $B$ Webs

    math.RT 2026-07 conditional novelty 7.0 of 10

    Type B webs give a complete diagrammatic presentation of the subcategory of U_q(so_{2n+1})-representations generated by the fundamental representations.

  2. Affine web of type Q

    math.RT 2025-06 conditional novelty 6.0 of 10

    The affine web category of type Q is defined, given a simplified presentation over C, and shown to have an integral diagrammatic basis indexed by elementary chicken foot diagrams.

  3. A Coboundary Temperely-Lieb Category for $\mathfrak{sl}_2$-Crystals

    math.RT 2025-02 conditional novelty 6.0 of 10

    A q=0 Temperley-Lieb category with explicit Jones-Wenzl projectors is shown to be equivalent as a coboundary category to sl2-crystals, yielding diagrammatic formulas for the crystal commutor.

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