{"title":"A Boson-fermion Realization of Highest Weight Modules over \\(\\mathfrak{g}\\widetilde{\\mathfrak{l}_{M/N}}(\\theta)\\)","authors":"Fu Lin Chen, Xin Huang, Shao Bin Tan","doi":"10.1007/s10114-024-3583-2","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we construct a superfermionic representation as well as a vertex representation for twisted general linear affine Lie superalgebras. We also establish a module isomorphism between them, which generalizes the super boson-fermion correspondence of type <i>B</i> given by Kac-van de Leur. Based on this isomorphism, we determine explicitly the irreducible components of these two representations. Particularly, we obtain in this way two kinds of systematic construction of level 1 irreducible integrable highest weight modules for twisted general linear affine Lie superalgebras.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"40 12","pages":"2879 - 2903"},"PeriodicalIF":0.8000,"publicationDate":"2024-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica Sinica-English Series","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10114-024-3583-2","RegionNum":3,"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
In this paper, we construct a superfermionic representation as well as a vertex representation for twisted general linear affine Lie superalgebras. We also establish a module isomorphism between them, which generalizes the super boson-fermion correspondence of type B given by Kac-van de Leur. Based on this isomorphism, we determine explicitly the irreducible components of these two representations. Particularly, we obtain in this way two kinds of systematic construction of level 1 irreducible integrable highest weight modules for twisted general linear affine Lie superalgebras.
本文构造了扭曲一般线性仿射李超代数的超费米子表示和顶点表示。我们还建立了它们之间的模同构，推广了Kac-van de Leur给出的B型超玻色子-费米子对应关系。基于这种同构性，我们明确地确定了这两种表示的不可约分量。特别地，我们用这种方法得到了扭转一般线性仿射李超代数的两种一级不可约可积最高权模的系统构造。
期刊介绍：
Acta Mathematica Sinica, established by the Chinese Mathematical Society in 1936, is the first and the best mathematical journal in China. In 1985, Acta Mathematica Sinica is divided into English Series and Chinese Series. The English Series is a monthly journal, publishing significant research papers from all branches of pure and applied mathematics. It provides authoritative reviews of current developments in mathematical research. Contributions are invited from researchers from all over the world.
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