{"title":"具有非球面参数的环切有理Cherednik代数的表示","authors":"Huijun Zhao","doi":"10.17760/d20291522","DOIUrl":null,"url":null,"abstract":"In this article, we describe all two sided ideals of a cyclotomic rational Cherednik algebra $H_\\mathbf{c}$ and its spherical subalgebra $eH_\\mathbf{c} e$ with a Weil generic aspherical parameter $\\mathbf{c}$, and further describe the simple modules in the category $\\mathcal{O}^{sph}_\\mathbf{c}$ . The main tools we use are categorical Kac-Moody actions on catogories $\\mathcal{O}_\\mathbf{c}$ and restriction functors for Harish-Chandra bimodules.","PeriodicalId":275006,"journal":{"name":"arXiv: Representation Theory","volume":"193 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2018-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Representations of cyclotomic rational Cherednik algebras with aspherical parameters\",\"authors\":\"Huijun Zhao\",\"doi\":\"10.17760/d20291522\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this article, we describe all two sided ideals of a cyclotomic rational Cherednik algebra $H_\\\\mathbf{c}$ and its spherical subalgebra $eH_\\\\mathbf{c} e$ with a Weil generic aspherical parameter $\\\\mathbf{c}$, and further describe the simple modules in the category $\\\\mathcal{O}^{sph}_\\\\mathbf{c}$ . The main tools we use are categorical Kac-Moody actions on catogories $\\\\mathcal{O}_\\\\mathbf{c}$ and restriction functors for Harish-Chandra bimodules.\",\"PeriodicalId\":275006,\"journal\":{\"name\":\"arXiv: Representation Theory\",\"volume\":\"193 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-08-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: Representation Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.17760/d20291522\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: Representation Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.17760/d20291522","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Representations of cyclotomic rational Cherednik algebras with aspherical parameters
In this article, we describe all two sided ideals of a cyclotomic rational Cherednik algebra $H_\mathbf{c}$ and its spherical subalgebra $eH_\mathbf{c} e$ with a Weil generic aspherical parameter $\mathbf{c}$, and further describe the simple modules in the category $\mathcal{O}^{sph}_\mathbf{c}$ . The main tools we use are categorical Kac-Moody actions on catogories $\mathcal{O}_\mathbf{c}$ and restriction functors for Harish-Chandra bimodules.
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