Heisenberg群扩展的Hecke-Baxter算子

IF 1.4 3区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL
A. A. Gerasimov, D. R. Lebedev, S. V. Oblezin
{"title":"Heisenberg群扩展的Hecke-Baxter算子","authors":"A. A. Gerasimov,&nbsp;D. R. Lebedev,&nbsp;S. V. Oblezin","doi":"10.1007/s11005-025-01971-8","DOIUrl":null,"url":null,"abstract":"<div><p>The <span>\\(GL_{\\ell +1}(\\mathbb {R})\\)</span> Hecke-Baxter operator was introduced as an element of the <span>\\(O_{\\ell +1}\\)</span>-spherical Hecke algebra associated with the Gelfand pair <span>\\(O_{\\ell +1}\\subset GL_{\\ell +1}(\\mathbb {R})\\)</span>. It was specified by the property to act on an <span>\\(O_{\\ell +1}\\)</span>-fixed vector in a <span>\\(GL_{\\ell +1}(\\mathbb {R})\\)</span>-principal series representation via multiplication by the local Archimedean <i>L</i>-factor canonically attached to the representation. In this note we propose another way to define the Hecke-Baxter operator, identifying it with a generalized Whittaker function for an extension of the Lie group <span>\\(GL_{\\ell +1}(\\mathbb {R})\\times GL_{\\ell +1}(\\mathbb {R})\\)</span> by a Heisenberg Lie group. We also show how this Whittaker function can be lifted to a matrix element of an extension of the Lie group <span>\\(Sp_{2\\ell +2}(\\mathbb {R})\\times Sp_{2\\ell +2}(\\mathbb {R})\\)</span> by a Heisenberg Lie group.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"115 4","pages":""},"PeriodicalIF":1.4000,"publicationDate":"2025-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Hecke-Baxter operators via Heisenberg group extensions\",\"authors\":\"A. A. Gerasimov,&nbsp;D. R. Lebedev,&nbsp;S. V. Oblezin\",\"doi\":\"10.1007/s11005-025-01971-8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The <span>\\\\(GL_{\\\\ell +1}(\\\\mathbb {R})\\\\)</span> Hecke-Baxter operator was introduced as an element of the <span>\\\\(O_{\\\\ell +1}\\\\)</span>-spherical Hecke algebra associated with the Gelfand pair <span>\\\\(O_{\\\\ell +1}\\\\subset GL_{\\\\ell +1}(\\\\mathbb {R})\\\\)</span>. It was specified by the property to act on an <span>\\\\(O_{\\\\ell +1}\\\\)</span>-fixed vector in a <span>\\\\(GL_{\\\\ell +1}(\\\\mathbb {R})\\\\)</span>-principal series representation via multiplication by the local Archimedean <i>L</i>-factor canonically attached to the representation. In this note we propose another way to define the Hecke-Baxter operator, identifying it with a generalized Whittaker function for an extension of the Lie group <span>\\\\(GL_{\\\\ell +1}(\\\\mathbb {R})\\\\times GL_{\\\\ell +1}(\\\\mathbb {R})\\\\)</span> by a Heisenberg Lie group. We also show how this Whittaker function can be lifted to a matrix element of an extension of the Lie group <span>\\\\(Sp_{2\\\\ell +2}(\\\\mathbb {R})\\\\times Sp_{2\\\\ell +2}(\\\\mathbb {R})\\\\)</span> by a Heisenberg Lie group.</p></div>\",\"PeriodicalId\":685,\"journal\":{\"name\":\"Letters in Mathematical Physics\",\"volume\":\"115 4\",\"pages\":\"\"},\"PeriodicalIF\":1.4000,\"publicationDate\":\"2025-07-12\",\"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/s11005-025-01971-8\",\"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}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Letters in Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s11005-025-01971-8","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

摘要

引入\(GL_{\ell +1}(\mathbb {R})\) Hecke- baxter算子作为与Gelfand对\(O_{\ell +1}\subset GL_{\ell +1}(\mathbb {R})\)相关的\(O_{\ell +1}\) -球面Hecke代数的一个元素。它是由属性指定的,通过乘以通常附加在表示上的局部阿基米德l因子,作用于\(GL_{\ell +1}(\mathbb {R})\)主级数表示中的\(O_{\ell +1}\)固定向量。在本文中,我们提出了另一种定义Hecke-Baxter算子的方法,即用一个广义Whittaker函数对李群\(GL_{\ell +1}(\mathbb {R})\times GL_{\ell +1}(\mathbb {R})\)通过Heisenberg李群的扩展进行标识。我们还展示了这个Whittaker函数如何被Heisenberg李群提升为李群\(Sp_{2\ell +2}(\mathbb {R})\times Sp_{2\ell +2}(\mathbb {R})\)扩展的矩阵元素。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
The Hecke-Baxter operators via Heisenberg group extensions

The \(GL_{\ell +1}(\mathbb {R})\) Hecke-Baxter operator was introduced as an element of the \(O_{\ell +1}\)-spherical Hecke algebra associated with the Gelfand pair \(O_{\ell +1}\subset GL_{\ell +1}(\mathbb {R})\). It was specified by the property to act on an \(O_{\ell +1}\)-fixed vector in a \(GL_{\ell +1}(\mathbb {R})\)-principal series representation via multiplication by the local Archimedean L-factor canonically attached to the representation. In this note we propose another way to define the Hecke-Baxter operator, identifying it with a generalized Whittaker function for an extension of the Lie group \(GL_{\ell +1}(\mathbb {R})\times GL_{\ell +1}(\mathbb {R})\) by a Heisenberg Lie group. We also show how this Whittaker function can be lifted to a matrix element of an extension of the Lie group \(Sp_{2\ell +2}(\mathbb {R})\times Sp_{2\ell +2}(\mathbb {R})\) by a Heisenberg Lie group.

求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
Letters in Mathematical Physics
Letters in Mathematical Physics 物理-物理:数学物理
CiteScore
2.40
自引率
8.30%
发文量
111
审稿时长
3 months
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.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:604180095
Book学术官方微信