Affine and cyclotomic webs
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911358161780736 |
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| author | Song, Linliang Wang, Weiqiang |
| author_facet | Song, Linliang Wang, Weiqiang |
| contents | Generalizing the polynomial web category, we introduce a diagrammatic $\Bbbk$-linear monoidal category, the affine web category, for any commutative ring $\Bbbk$. Integral bases consisting of elementary diagrams are obtained for the affine web category and its cyclotomic quotient categories. Connections between cyclotomic web categories and finite $W$-algebras are established, leading to a diagrammatic presentation of idempotent subalgebras of $W$-Schur algebras introduced by Brundan-Kleshchev. The affine web category will be used as a basic building block of another $\Bbbk$-linear monoidal category, the affine Schur category, formulated in a sequel. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_13172 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Affine and cyclotomic webs Song, Linliang Wang, Weiqiang Representation Theory Quantum Algebra Generalizing the polynomial web category, we introduce a diagrammatic $\Bbbk$-linear monoidal category, the affine web category, for any commutative ring $\Bbbk$. Integral bases consisting of elementary diagrams are obtained for the affine web category and its cyclotomic quotient categories. Connections between cyclotomic web categories and finite $W$-algebras are established, leading to a diagrammatic presentation of idempotent subalgebras of $W$-Schur algebras introduced by Brundan-Kleshchev. The affine web category will be used as a basic building block of another $\Bbbk$-linear monoidal category, the affine Schur category, formulated in a sequel. |
| title | Affine and cyclotomic webs |
| topic | Representation Theory Quantum Algebra |
| url | https://arxiv.org/abs/2406.13172 |