{"title":"Calogero–Moser eigenfunctions modulo \\(p^s\\)","authors":"Alexander Gorsky, Alexander Varchenko","doi":"10.1007/s11005-024-01792-1","DOIUrl":null,"url":null,"abstract":"<div><p>In this note we use the Matsuo–Cherednik duality between the solutions to the Knizhnik–Zamolodchikov (KZ) equations and eigenfunctions of Calogero–Moser Hamiltonians to get the polynomial <span>\\(p^s\\)</span>-truncation of the Calogero–Moser eigenfunctions at a rational coupling constant. The truncation procedure uses the integral representation for the hypergeometric solutions to KZ equations. The <span>\\(s\\rightarrow \\infty \\)</span> limit to the pure <i>p</i>-adic case has been analyzed in the <span>\\(n=2\\)</span> case.\n</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 2","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Letters in Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s11005-024-01792-1","RegionNum":3,"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
In this note we use the Matsuo–Cherednik duality between the solutions to the Knizhnik–Zamolodchikov (KZ) equations and eigenfunctions of Calogero–Moser Hamiltonians to get the polynomial \(p^s\)-truncation of the Calogero–Moser eigenfunctions at a rational coupling constant. The truncation procedure uses the integral representation for the hypergeometric solutions to KZ equations. The \(s\rightarrow \infty \) limit to the pure p-adic case has been analyzed in the \(n=2\) case.
在这篇论文中，我们利用克尼日尼克-扎莫洛奇科夫（Knizhnik-Zamolodchikov，KZ）方程的解与卡洛吉罗-莫瑟哈密顿的特征函数之间的马祖-切列德尼克对偶性，得到了卡洛吉罗-莫瑟特征函数在有理耦合常数处的多（p^s\）-截断（polynomial \(p^s\)-truncation of the Calogero-Moser eigenfunctions at a rational coupling constant）。截断过程使用的是 KZ 方程超几何解的积分表示法。在(n=2\)情况下分析了纯p-adic情况的(s\rightarrow \infty\)极限。
期刊介绍：
The aim of Letters in Mathematical Physics is to attract the community''s attention on important and original developments in the area of mathematical physics and contemporary theoretical physics. The journal publishes letters and longer research articles, occasionally also articles containing topical reviews. We are committed to both fast publication and careful refereeing. In addition, the journal offers important contributions to modern mathematics in fields which have a potential physical application, and important developments in theoretical physics which have potential mathematical impact.
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