Affine and cyclotomic webs
| Autor: | Song, Linliang, Wang, Weiqiang |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 46 pages, many figures |
| Databáze: | arXiv |
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