{"title":"Whittaker Modules Over Some Generalized Weyl Algebras","authors":"Hongjia Chen, Longhui Wang","doi":"10.1007/s10468-023-10200-6","DOIUrl":null,"url":null,"abstract":"<div><p>In Benkart and Ondrus (Represent. Theory <b>13</b>, 141–164 2009), Benkart and Ondrus investigated Whittaker modules for generalized Weyl algebras. Following the results of Benkart and Ondrus, we study Whittaker modules for three special kinds of generalized Weyl algebras in this note, including Rueda’s algebras, the algebras <i>U</i><sub><i>q</i></sub>(<i>f</i>(<i>K</i>)) and <i>U</i><sub><i>q</i></sub>(<i>f</i>(<i>K</i>,<i>H</i>)). In particular, we acquire the centers of the last two classes of algebras before giving an explicit description of their simple Whittaker modules.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"26 6","pages":"3047 - 3064"},"PeriodicalIF":0.6000,"publicationDate":"2023-02-15","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/s10468-023-10200-6","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In Benkart and Ondrus (Represent. Theory 13, 141–164 2009), Benkart and Ondrus investigated Whittaker modules for generalized Weyl algebras. Following the results of Benkart and Ondrus, we study Whittaker modules for three special kinds of generalized Weyl algebras in this note, including Rueda’s algebras, the algebras Uq(f(K)) and Uq(f(K,H)). In particular, we acquire the centers of the last two classes of algebras before giving an explicit description of their simple Whittaker 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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