{"title":"Generalized theta series and monodromy of a Casimir connection. Case of rank 1","authors":"E. I. Dotsenko","doi":"10.1134/S0040577924050015","DOIUrl":null,"url":null,"abstract":"<p> The monodromy of the <span>\\(\\mathfrak{sl}(2)\\)</span> Casimir connection is considered. It is shown that the trace of the monodromy operator over an appropriate space of flat sections gives the Jacobi theta constant and incomplete theta functions. A definition of new objects, namely, incomplete Appell–Lerch sums, is given, and their connection with the trace of the monodromy operator is revealed. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"219 2","pages":"705 - 711"},"PeriodicalIF":1.0000,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theoretical and Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1134/S0040577924050015","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
The monodromy of the \(\mathfrak{sl}(2)\) Casimir connection is considered. It is shown that the trace of the monodromy operator over an appropriate space of flat sections gives the Jacobi theta constant and incomplete theta functions. A definition of new objects, namely, incomplete Appell–Lerch sums, is given, and their connection with the trace of the monodromy operator is revealed.
Abstract The monodromy of the \(\mathfrak{sl}(2)\)卡西米尔连接进行了研究。研究表明，在适当的平面截面空间上的单反转算子的迹给出了雅可比 Theta 常量和不完全 Theta 函数。给出了新对象的定义，即不完全阿贝尔-勒奇和，并揭示了它们与单旋转算子迹的联系。
期刊介绍：
Theoretical and Mathematical Physics covers quantum field theory and theory of elementary particles, fundamental problems of nuclear physics, many-body problems and statistical physics, nonrelativistic quantum mechanics, and basic problems of gravitation theory. Articles report on current developments in theoretical physics as well as related mathematical problems.
Theoretical and Mathematical Physics is published in collaboration with the Steklov Mathematical Institute of the Russian Academy of Sciences.
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