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arXiv · 2602.11479

Modules of the Temperley-Lieb algebra at zero

Eddy Li·Kenta Suzuki
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Abstract

We explicitly describe the category of modules of the Temperley-Lieb algebra $\mathrm{TL}_n(\beta)$ under specialization $\beta=0$ 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.

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Eddy Li, Kenta Suzuki. 2026-02-12. Modules of the Temperley-Lieb algebra at zero. https://arxiv.org/abs/2602.11479

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