{"title":"Monomial realizations and LS paths of fundamental representations for rank 2 Kac-Moody algebras","authors":"Yuki Kanakubo","doi":"10.1016/j.jalgebra.2025.01.032","DOIUrl":null,"url":null,"abstract":"<div><div>For a Kac-Moody algebra <span><math><mi>g</mi></math></span> of rank 2 and a fundamental weight <em>λ</em>, we explicitly give an isomorphism between the set of Lakshmibai-Seshadri paths <span><math><mi>B</mi><mo>(</mo><mi>λ</mi><mo>)</mo></math></span> and monomial realization <span><math><mi>M</mi><mo>(</mo><mi>λ</mi><mo>)</mo></math></span>. As an application, we also give an explicit form of monomial realization <span><math><mi>M</mi><mo>(</mo><mi>λ</mi><mo>)</mo></math></span> in terms of Weyl groups.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"672 ","pages":"Pages 31-49"},"PeriodicalIF":0.8000,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Algebra","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0021869325000833","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
For a Kac-Moody algebra of rank 2 and a fundamental weight λ, we explicitly give an isomorphism between the set of Lakshmibai-Seshadri paths and monomial realization . As an application, we also give an explicit form of monomial realization in terms of Weyl groups.
期刊介绍：
The Journal of Algebra is a leading international journal and publishes papers that demonstrate high quality research results in algebra and related computational aspects. Only the very best and most interesting papers are to be considered for publication in the journal. With this in mind, it is important that the contribution offer a substantial result that will have a lasting effect upon the field. The journal also seeks work that presents innovative techniques that offer promising results for future research.
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