{"title":"反射子群的归一化器的编织群","authors":"T. Gobet, A. Henderson, Ivan Marin","doi":"10.5802/aif.3440","DOIUrl":null,"url":null,"abstract":"Let $W_0$ be a reflection subgroup of a finite complex reflection group $W$, and let $B_0$ and $B$ be their respective braid groups. In order to construct a Hecke algebra $\\widetilde{H}_0$ for the normalizer $N_W(W_0)$, one first considers a natural subquotient $\\widetilde{B}_0$ of $B$ which is an extension of $N_W(W_0)/W_0$ by $B_0$. We prove that this extension is split when $W$ is a Coxeter group, and deduce a standard basis for the Hecke algebra $\\widetilde{H}_0$. We also give classes of both split and non-split examples in the non-Coxeter case.","PeriodicalId":50781,"journal":{"name":"Annales De L Institut Fourier","volume":" ","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2020-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Braid groups of normalizers of reflection subgroups\",\"authors\":\"T. Gobet, A. Henderson, Ivan Marin\",\"doi\":\"10.5802/aif.3440\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let $W_0$ be a reflection subgroup of a finite complex reflection group $W$, and let $B_0$ and $B$ be their respective braid groups. In order to construct a Hecke algebra $\\\\widetilde{H}_0$ for the normalizer $N_W(W_0)$, one first considers a natural subquotient $\\\\widetilde{B}_0$ of $B$ which is an extension of $N_W(W_0)/W_0$ by $B_0$. We prove that this extension is split when $W$ is a Coxeter group, and deduce a standard basis for the Hecke algebra $\\\\widetilde{H}_0$. We also give classes of both split and non-split examples in the non-Coxeter case.\",\"PeriodicalId\":50781,\"journal\":{\"name\":\"Annales De L Institut Fourier\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2020-02-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annales De L Institut Fourier\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.5802/aif.3440\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annales De L Institut Fourier","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.5802/aif.3440","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Braid groups of normalizers of reflection subgroups
Let $W_0$ be a reflection subgroup of a finite complex reflection group $W$, and let $B_0$ and $B$ be their respective braid groups. In order to construct a Hecke algebra $\widetilde{H}_0$ for the normalizer $N_W(W_0)$, one first considers a natural subquotient $\widetilde{B}_0$ of $B$ which is an extension of $N_W(W_0)/W_0$ by $B_0$. We prove that this extension is split when $W$ is a Coxeter group, and deduce a standard basis for the Hecke algebra $\widetilde{H}_0$. We also give classes of both split and non-split examples in the non-Coxeter case.
期刊介绍:
The Annales de l’Institut Fourier aim at publishing original papers of a high level in all fields of mathematics, either in English or in French.
The Editorial Board encourages submission of articles containing an original and important result, or presenting a new proof of a central result in a domain of mathematics. Also, the Annales de l’Institut Fourier being a general purpose journal, highly specialized articles can only be accepted if their exposition makes them accessible to a larger audience.