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arXiv · 2210.09289

A comparison between $SL_n$ spider categories

Anup Poudel
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Abstract

We prove a conjecture of L\^{e} and Sikora by providing a comparison between various existing $SL_n$ skein theories. While doing so, we show that the full subcategory of the spider category, $\mathcal{S}p(SL_n)$, defined by Cautis-Kamnitzer-Morrison, whose objects are monoidally generated by the standard representation and its dual, is equivalent as a spherical braided category to Sikora's quotient category. This also answers a question from Morrison's Ph.D. thesis. Finally, we show that the skein modules associated to the CKM and Sikora's webs are isomorphic.

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Anup Poudel. 2022-10-17. A comparison between $SL_n$ spider categories. https://doi.org/10.4153/s0008414x25000240

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