Existence and rotatability of the two-colored Jones-Wenzl projector
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866929274349420544 |
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| author | Hazi, Amit |
| author_facet | Hazi, Amit |
| contents | The two-colored Temperley-Lieb algebra $2\mathrm{TL}_R({}_s {n})$ is a generalization of the Temperley-Lieb algebra. The analogous two-colored Jones-Wenzl projector $\mathrm{JW}_R({}_s {n}) \in 2\mathrm{TL}_R({}_s {n})$ plays an important role in the Elias-Williamson construction of the diagrammatic Hecke category. We give conditions for the existence and rotatability of $\mathrm{JW}_R({}_s {n})$ in terms of the invertibility and vanishing of certain two-colored quantum binomial coefficients. As a consequence, we prove that Abe's category of Soergel bimodules is equivalent to the diagrammatic Hecke category in complete generality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_14476 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Existence and rotatability of the two-colored Jones-Wenzl projector Hazi, Amit Representation Theory Quantum Algebra Primary 20G42, 20F55, Secondary 11R18 The two-colored Temperley-Lieb algebra $2\mathrm{TL}_R({}_s {n})$ is a generalization of the Temperley-Lieb algebra. The analogous two-colored Jones-Wenzl projector $\mathrm{JW}_R({}_s {n}) \in 2\mathrm{TL}_R({}_s {n})$ plays an important role in the Elias-Williamson construction of the diagrammatic Hecke category. We give conditions for the existence and rotatability of $\mathrm{JW}_R({}_s {n})$ in terms of the invertibility and vanishing of certain two-colored quantum binomial coefficients. As a consequence, we prove that Abe's category of Soergel bimodules is equivalent to the diagrammatic Hecke category in complete generality. |
| title | Existence and rotatability of the two-colored Jones-Wenzl projector |
| topic | Representation Theory Quantum Algebra Primary 20G42, 20F55, Secondary 11R18 |
| url | https://arxiv.org/abs/2302.14476 |