{"title":"Finite Young wall model for representations of $$\\imath $$ quantum group $${\\textbf{U}}^{\\jmath }$$","authors":"Shaolong Han","doi":"10.1007/s10801-023-01292-w","DOIUrl":null,"url":null,"abstract":"<p>We construct a finite Young wall model for a certain irreducible module over <span>\\(\\imath \\)</span>quantum group <span>\\({\\textbf{U}}^{\\jmath }\\)</span>. Moreover, we show that this irreducible module is a highest weight module and is determined by a crystal structure on the set of finite Young walls.</p>","PeriodicalId":14926,"journal":{"name":"Journal of Algebraic Combinatorics","volume":"1 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2024-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Algebraic Combinatorics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10801-023-01292-w","RegionNum":3,"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
We construct a finite Young wall model for a certain irreducible module over \(\imath \)quantum group \({\textbf{U}}^{\jmath }\). Moreover, we show that this irreducible module is a highest weight module and is determined by a crystal structure on the set of finite Young walls.
期刊介绍:
The Journal of Algebraic Combinatorics provides a single forum for papers on algebraic combinatorics which, at present, are distributed throughout a number of journals. Within the last decade or so, algebraic combinatorics has evolved into a mature, established and identifiable area of mathematics. Research contributions in the field are increasingly seen to have substantial links with other areas of mathematics.
The journal publishes papers in which combinatorics and algebra interact in a significant and interesting fashion. This interaction might occur through the study of combinatorial structures using algebraic methods, or the application of combinatorial methods to algebraic problems.