{"title":"A vertex operator reformulation of the Kanade–Russell conjecture modulo 9","authors":"Shunsuke Tsuchioka","doi":"10.1007/s11139-024-00895-6","DOIUrl":null,"url":null,"abstract":"<p>We reformulate the Kanade–Russell conjecture modulo 9 via the vertex operators for the level 3 standard modules of type <span>\\(D^{(3)}_{4}\\)</span>. Along the same lines, we arrive at three partition theorems which may be regarded as an <span>\\(A^{(2)}_{4}\\)</span> analog of the conjecture. Andrews–van Ekeren–Heluani have proven one of them, and we point out that the others are easily proven from their results.</p>","PeriodicalId":501430,"journal":{"name":"The Ramanujan Journal","volume":"30 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"The Ramanujan Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s11139-024-00895-6","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
We reformulate the Kanade–Russell conjecture modulo 9 via the vertex operators for the level 3 standard modules of type \(D^{(3)}_{4}\). Along the same lines, we arrive at three partition theorems which may be regarded as an \(A^{(2)}_{4}\) analog of the conjecture. Andrews–van Ekeren–Heluani have proven one of them, and we point out that the others are easily proven from their results.
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