Philippe Di Francesco, Rinat Kedem, Sergey Khoroshkin, Gus Schrader, Alexander Shapiro
{"title":"Ruijsenaars wavefunctions as modular group matrix coefficients","authors":"Philippe Di Francesco, Rinat Kedem, Sergey Khoroshkin, Gus Schrader, Alexander Shapiro","doi":"10.1007/s11005-024-01881-1","DOIUrl":null,"url":null,"abstract":"<div><p>We give a description of the Hallnäs–Ruijsenaars eigenfunctions of the 2-particle hyperbolic Ruijsenaars system as matrix coefficients for the order 4 element <span>\\(S\\in SL(2,{\\mathbb {Z}})\\)</span> acting on the Hilbert space of <i>GL</i>(2) quantum Teichmüller theory on the punctured torus. The <i>GL</i>(2) Macdonald polynomials are then obtained as special values of the analytic continuation of these matrix coefficients. The main tool used in the proof is the cluster structure on the moduli space of framed <i>GL</i>(2)-local systems on the punctured torus, and an <span>\\(SL(2,{\\mathbb {Z}})\\)</span>-equivariant embedding of the <i>GL</i>(2) spherical DAHA into the quantized coordinate ring of the corresponding cluster Poisson variety.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 6","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2024-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-024-01881-1.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Letters in Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s11005-024-01881-1","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
We give a description of the Hallnäs–Ruijsenaars eigenfunctions of the 2-particle hyperbolic Ruijsenaars system as matrix coefficients for the order 4 element \(S\in SL(2,{\mathbb {Z}})\) acting on the Hilbert space of GL(2) quantum Teichmüller theory on the punctured torus. The GL(2) Macdonald polynomials are then obtained as special values of the analytic continuation of these matrix coefficients. The main tool used in the proof is the cluster structure on the moduli space of framed GL(2)-local systems on the punctured torus, and an \(SL(2,{\mathbb {Z}})\)-equivariant embedding of the GL(2) spherical DAHA into the quantized coordinate ring of the corresponding cluster Poisson variety.
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.