Affine and cyclotomic webs

IF 1.2 2区数学 Q1 MATHEMATICS

Journal of the London Mathematical Society-Second Series Pub Date : 2025-09-08 DOI:10.1112/jlms.70278

Linliang Song, Weiqiang Wang

{"title":"Affine and cyclotomic webs","authors":"Linliang Song, Weiqiang Wang","doi":"10.1112/jlms.70278","DOIUrl":null,"url":null,"abstract":"Generalizing the polynomial web category, we introduce a diagrammatic <math>\n <semantics>\n <mi>k</mi>\n <annotation>$\\mathbb {k}$</annotation>\n </semantics></math>-linear monoidal category, the affine web category, for any commutative ring <math>\n <semantics>\n <mi>k</mi>\n <annotation>$\\mathbb {k}$</annotation>\n </semantics></math>. 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 <math>\n <semantics>\n <mi>W</mi>\n <annotation>$W$</annotation>\n </semantics></math>-algebras are established, leading to a diagrammatic presentation of idempotent subalgebras of <math>\n <semantics>\n <mi>W</mi>\n <annotation>$W$</annotation>\n </semantics></math>-Schur algebras introduced by Brundan–Kleshchev. The affine web category will be used as a basic building block of another <math>\n <semantics>\n <mi>k</mi>\n <annotation>$\\mathbb {k}$</annotation>\n </semantics></math>-linear monoidal category, the affine Schur category, formulated in a sequel.","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 3","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2025-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the London Mathematical Society-Second Series","FirstCategoryId":"100","ListUrlMain":"https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/jlms.70278","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

Abstract

Generalizing the polynomial web category, we introduce a diagrammatic $k$ -linear monoidal category, the affine web category, for any commutative ring $k$ . 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 $k$ -linear monoidal category, the affine Schur category, formulated in a sequel.

Abstract Image

查看原文本刊更多论文

仿射和切环网

推广多项式网范畴，对任意可交换环k $\mathbb {k}$引入一个图k $\mathbb {k}$线性一元范畴仿射网范畴。得到了仿射网类及其环商类由初等图组成的积分基。建立了分环网范畴与有限W$ W$ -代数之间的联系，得到了Brundan-Kleshchev引入的W$ W$ -Schur代数的幂等子代数的图解表示。仿射网络范畴将被用作另一个k $\mathbb {k}$线性一元范畴的基本构建块，仿射舒尔范畴，在续集中表述。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Journal of the London Mathematical Society-Second Series 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

186

审稿时长

6-12 weeks

期刊介绍： The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.