A comparison between $SL_n$ spider categories
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866916918529622016 |
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| author | Poudel, Anup |
| author_facet | Poudel, Anup |
| contents | We prove a conjecture of Lê 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_09289 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A comparison between $SL_n$ spider categories Poudel, Anup Geometric Topology Quantum Algebra We prove a conjecture of Lê 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. |
| title | A comparison between $SL_n$ spider categories |
| topic | Geometric Topology Quantum Algebra |
| url | https://arxiv.org/abs/2210.09289 |