Cell modules for the Temperley-Lieb algebra in mixed characteristic
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918303700615168 |
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| author | Martin, Stuart Senécal, Charles Spencer, Robert A. |
| author_facet | Martin, Stuart Senécal, Charles Spencer, Robert A. |
| contents | We study the representation theory of the Temperley-Lieb algebra $\mathsf{TL}_n^k(δ)$ in mixed characteristic, i.e. over an arbitrary field $k$ of characteristic $p$ and where $δ$ satisfies some minimal polynomial $m_δ$. In particular, we completely describe the submodule structure of cell modules for $\mathsf{TL}_n$ and give their Alperin diagrams. The proof is entirely diagrammatic and does not appeal to the role of $\mathsf{TL}_n$ as the endomorphism algebra of tensor powers of the fundamental representation of $\textbf{U}_q(\mathfrak{sl}_2)$. We also investigate two-dimensional Jantzen-like filtrations of the cell modules related to the mixed characteristic. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_17445 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Cell modules for the Temperley-Lieb algebra in mixed characteristic Martin, Stuart Senécal, Charles Spencer, Robert A. Representation Theory We study the representation theory of the Temperley-Lieb algebra $\mathsf{TL}_n^k(δ)$ in mixed characteristic, i.e. over an arbitrary field $k$ of characteristic $p$ and where $δ$ satisfies some minimal polynomial $m_δ$. In particular, we completely describe the submodule structure of cell modules for $\mathsf{TL}_n$ and give their Alperin diagrams. The proof is entirely diagrammatic and does not appeal to the role of $\mathsf{TL}_n$ as the endomorphism algebra of tensor powers of the fundamental representation of $\textbf{U}_q(\mathfrak{sl}_2)$. We also investigate two-dimensional Jantzen-like filtrations of the cell modules related to the mixed characteristic. |
| title | Cell modules for the Temperley-Lieb algebra in mixed characteristic |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2601.17445 |