Modules of the Temperley-Lieb algebra at zero
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917269838233600 |
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| author | Li, Eddy Suzuki, Kenta |
| author_facet | Li, Eddy Suzuki, Kenta |
| contents | We explicitly describe the category of modules of the Temperley-Lieb algebra $\mathrm{TL}_n(β)$ under specialization $β=0$ for even $n$ in terms of a quiver algebra, analogous to a result of Berest-Etingof-Ginzburg. In particular, we explicitly construct an exact sequence of the standard modules of $\mathrm{TL}_n(0)$, which categorifies a numerical coincidence regarding the evaluation of the Jones polynomial at $t=-1$. We furthermore deduce a consequence in the representation theory of symmetric groups over characteristic two. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_11479 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Modules of the Temperley-Lieb algebra at zero Li, Eddy Suzuki, Kenta Representation Theory Quantum Algebra We explicitly describe the category of modules of the Temperley-Lieb algebra $\mathrm{TL}_n(β)$ under specialization $β=0$ for even $n$ in terms of a quiver algebra, analogous to a result of Berest-Etingof-Ginzburg. In particular, we explicitly construct an exact sequence of the standard modules of $\mathrm{TL}_n(0)$, which categorifies a numerical coincidence regarding the evaluation of the Jones polynomial at $t=-1$. We furthermore deduce a consequence in the representation theory of symmetric groups over characteristic two. |
| title | Modules of the Temperley-Lieb algebra at zero |
| topic | Representation Theory Quantum Algebra |
| url | https://arxiv.org/abs/2602.11479 |