{"title":"On the Mathieu conjecture for Sp(N) and G2","authors":"Kevin Zwart","doi":"10.1063/5.0206983","DOIUrl":null,"url":null,"abstract":"As a direct continuation of Zwart [J. Math. Phys. 64(10), 101701 (2023)], which is built on the work of Müger and Tuset [Indagationes Math. 35(1), 114 (2024)], we reduce the Mathieu conjecture, formulated by Mathieu [Algèbra Non Commutative, Groupes Quantiques et Invariants, edited by Alex, J. and Cauchon, G. (Société Mathématique de France, Reims, 1997), Vol. 2, pp. 263–279], for Sp(N) and G2 to a conjecture involving functions over Rn×(S1)m with n,m∈N0. The proofs rely on Euler-style parametrizations of these groups, a specific version of the KAK decomposition, which we discuss and prove.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.2000,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1063/5.0206983","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
As a direct continuation of Zwart [J. Math. Phys. 64(10), 101701 (2023)], which is built on the work of Müger and Tuset [Indagationes Math. 35(1), 114 (2024)], we reduce the Mathieu conjecture, formulated by Mathieu [Algèbra Non Commutative, Groupes Quantiques et Invariants, edited by Alex, J. and Cauchon, G. (Société Mathématique de France, Reims, 1997), Vol. 2, pp. 263–279], for Sp(N) and G2 to a conjecture involving functions over Rn×(S1)m with n,m∈N0. The proofs rely on Euler-style parametrizations of these groups, a specific version of the KAK decomposition, which we discuss and prove.
作为 Zwart [J. Math. Phys. 64(10), 101701 (2023)]在 Müger 和 Tuset [Indagationes Math. 35(1), 114 (2024)]工作基础上的直接延续，我们将 Mathieu [Algèbra Non Commutative, Groupes Quantiques et Invariants, edited by Alex, J. and Cauchon, G. (Société Mathématique de France, Reims, 1997, Vol. 2, pp.and Cauchon, G. (Société Mathématique de France, Reims, 1997), Vol. 2, pp.证明依赖于这些群的欧拉式参数化，即 KAK 分解的一个特定版本，我们对其进行了讨论和证明。
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