{"title":"Affine \\(\\imath \\)Quantum Groups and Twisted Yangians in Drinfeld Presentations","authors":"Kang Lu, Weiqiang Wang, Weinan Zhang","doi":"10.1007/s00220-025-05263-z","DOIUrl":null,"url":null,"abstract":"<div><p>We formulate a family of algebras, twisted Yangians (of split type) in current generators and relations, via a degeneration of the Drinfeld presentation of affine <span>\\(\\imath \\)</span>quantum groups (associated with split Satake diagrams). These new algebras admit PBW type bases and are shown to be a deformation of twisted current algebras; presentations for twisted current algebras are also provided. For type AI, it matches with the Drinfeld presentation of twisted Yangian obtained via Gauss decomposition. We conjecture that our split twisted Yangians are isomorphic to the corresponding ones in RTT presentation.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 5","pages":""},"PeriodicalIF":2.2000,"publicationDate":"2025-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s00220-025-05263-z","RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
We formulate a family of algebras, twisted Yangians (of split type) in current generators and relations, via a degeneration of the Drinfeld presentation of affine \(\imath \)quantum groups (associated with split Satake diagrams). These new algebras admit PBW type bases and are shown to be a deformation of twisted current algebras; presentations for twisted current algebras are also provided. For type AI, it matches with the Drinfeld presentation of twisted Yangian obtained via Gauss decomposition. We conjecture that our split twisted Yangians are isomorphic to the corresponding ones in RTT presentation.
期刊介绍:
The mission of Communications in Mathematical Physics is to offer a high forum for works which are motivated by the vision and the challenges of modern physics and which at the same time meet the highest mathematical standards.