{"title":"具有任意无穷小字符的惠特克模块的卡兹丹-卢兹蒂算法","authors":"Qixian Zhao","doi":"10.1007/s10468-023-10222-0","DOIUrl":null,"url":null,"abstract":"<div><p>Let <span>\\(\\mathfrak {g}\\)</span> be a complex semisimple Lie algebra. We give a description of characters of irreducible Whittaker modules for <span>\\(\\mathfrak {g}\\)</span> with any infinitesimal character, along with a Kazhdan-Lusztig algorithm for computing them. This generalizes Miličić-Soergel’s and Romanov’s results for integral infinitesimal characters. As a special case, we recover the non-integral Kazhdan-Lusztig conjecture for Verma modules.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"27 1","pages":"767 - 814"},"PeriodicalIF":0.5000,"publicationDate":"2023-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Kazhdan-Lusztig Algorithm for Whittaker Modules with Arbitrary Infinitesimal Characters\",\"authors\":\"Qixian Zhao\",\"doi\":\"10.1007/s10468-023-10222-0\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Let <span>\\\\(\\\\mathfrak {g}\\\\)</span> be a complex semisimple Lie algebra. We give a description of characters of irreducible Whittaker modules for <span>\\\\(\\\\mathfrak {g}\\\\)</span> with any infinitesimal character, along with a Kazhdan-Lusztig algorithm for computing them. This generalizes Miličić-Soergel’s and Romanov’s results for integral infinitesimal characters. As a special case, we recover the non-integral Kazhdan-Lusztig conjecture for Verma modules.</p></div>\",\"PeriodicalId\":50825,\"journal\":{\"name\":\"Algebras and Representation Theory\",\"volume\":\"27 1\",\"pages\":\"767 - 814\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2023-10-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Algebras and Representation Theory\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10468-023-10222-0\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Algebras and Representation Theory","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10468-023-10222-0","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Kazhdan-Lusztig Algorithm for Whittaker Modules with Arbitrary Infinitesimal Characters
Let \(\mathfrak {g}\) be a complex semisimple Lie algebra. We give a description of characters of irreducible Whittaker modules for \(\mathfrak {g}\) with any infinitesimal character, along with a Kazhdan-Lusztig algorithm for computing them. This generalizes Miličić-Soergel’s and Romanov’s results for integral infinitesimal characters. As a special case, we recover the non-integral Kazhdan-Lusztig conjecture for Verma modules.
期刊介绍：
Algebras and Representation Theory features carefully refereed papers relating, in its broadest sense, to the structure and representation theory of algebras, including Lie algebras and superalgebras, rings of differential operators, group rings and algebras, C*-algebras and Hopf algebras, with particular emphasis on quantum groups.
The journal contains high level, significant and original research papers, as well as expository survey papers written by specialists who present the state-of-the-art of well-defined subjects or subdomains. Occasionally, special issues on specific subjects are published as well, the latter allowing specialists and non-specialists to quickly get acquainted with new developments and topics within the field of rings, algebras and their applications.
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