Superalgebra deformations of web categories: Affine and cyclotomic webs
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912731013054464 |
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| author | Davidson, Nicholas Kujawa, Jonathan R. Muth, Robert |
| author_facet | Davidson, Nicholas Kujawa, Jonathan R. Muth, Robert |
| contents | Let $\mathbb{k}$ be a characteristic zero domain. We define and study a diagrammatic monoidal $\mathbb{k}$-linear supercategory $\mathbf{Web}^{aff}_{A}$ associated to any locally unital Frobenius $\mathbb{k}$-superalgebra $A$. This category can be viewed variously as an affinization of the finite web category $\mathbf{Web}_{A}$ previously defined by the authors and Zhu, as a thickening of the degenerate affine wreath product algebras defined by Savage, or as a Frobenius deformation of affine web categories defined by Song and Wang. We show that there is an asymptotically faithful family of functors from $\mathbf{Web}^{aff}_{A}$ to the monoidal supercategory of endofunctors of $\mathfrak{gl}_n(A)$-modules for every $n \geq 1$, and use this to establish a basis of `decorated double coset diagrams' for morphism spaces in $\mathbf{Web}^{aff}_{A}$. We also define and establish basis results for the cyclotomic quotient category $\mathbf{Web}^Λ_{A}$ associated with a cyclotomic datum $Λ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_21671 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Superalgebra deformations of web categories: Affine and cyclotomic webs Davidson, Nicholas Kujawa, Jonathan R. Muth, Robert Representation Theory 17B37, 16G99, 18D10, 20C33 Let $\mathbb{k}$ be a characteristic zero domain. We define and study a diagrammatic monoidal $\mathbb{k}$-linear supercategory $\mathbf{Web}^{aff}_{A}$ associated to any locally unital Frobenius $\mathbb{k}$-superalgebra $A$. This category can be viewed variously as an affinization of the finite web category $\mathbf{Web}_{A}$ previously defined by the authors and Zhu, as a thickening of the degenerate affine wreath product algebras defined by Savage, or as a Frobenius deformation of affine web categories defined by Song and Wang. We show that there is an asymptotically faithful family of functors from $\mathbf{Web}^{aff}_{A}$ to the monoidal supercategory of endofunctors of $\mathfrak{gl}_n(A)$-modules for every $n \geq 1$, and use this to establish a basis of `decorated double coset diagrams' for morphism spaces in $\mathbf{Web}^{aff}_{A}$. We also define and establish basis results for the cyclotomic quotient category $\mathbf{Web}^Λ_{A}$ associated with a cyclotomic datum $Λ$. |
| title | Superalgebra deformations of web categories: Affine and cyclotomic webs |
| topic | Representation Theory 17B37, 16G99, 18D10, 20C33 |
| url | https://arxiv.org/abs/2511.21671 |