{"title":"Characters of logarithmic vertex operator algebras and coloured invariants of torus links","authors":"S. Kanade","doi":"10.1090/bproc/223","DOIUrl":null,"url":null,"abstract":"<p>We show that the characters of <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"German s German l Subscript r\">\n <mml:semantics>\n <mml:msub>\n <mml:mrow class=\"MJX-TeXAtom-ORD\">\n <mml:mi mathvariant=\"fraktur\">s</mml:mi>\n <mml:mi mathvariant=\"fraktur\">l</mml:mi>\n </mml:mrow>\n <mml:mi>r</mml:mi>\n </mml:msub>\n <mml:annotation encoding=\"application/x-tex\">\\mathfrak {sl}_r</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula> versions of the <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"left-parenthesis 1 comma p right-parenthesis\">\n <mml:semantics>\n <mml:mrow>\n <mml:mo stretchy=\"false\">(</mml:mo>\n <mml:mn>1</mml:mn>\n <mml:mo>,</mml:mo>\n <mml:mi>p</mml:mi>\n <mml:mo stretchy=\"false\">)</mml:mo>\n </mml:mrow>\n <mml:annotation encoding=\"application/x-tex\">(1,p)</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula> singlet and the <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"left-parenthesis 1 comma p right-parenthesis\">\n <mml:semantics>\n <mml:mrow>\n <mml:mo stretchy=\"false\">(</mml:mo>\n <mml:mn>1</mml:mn>\n <mml:mo>,</mml:mo>\n <mml:mi>p</mml:mi>\n <mml:mo stretchy=\"false\">)</mml:mo>\n </mml:mrow>\n <mml:annotation encoding=\"application/x-tex\">(1,p)</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula> triplet vertex operator algebras arise as limits of appropriately coloured <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"German s German l Subscript r\">\n <mml:semantics>\n <mml:msub>\n <mml:mrow class=\"MJX-TeXAtom-ORD\">\n <mml:mi mathvariant=\"fraktur\">s</mml:mi>\n <mml:mi mathvariant=\"fraktur\">l</mml:mi>\n </mml:mrow>\n <mml:mi>r</mml:mi>\n </mml:msub>\n <mml:annotation encoding=\"application/x-tex\">\\mathfrak {sl}_r</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula> Jones invariants of certain torus links.</p>","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"2 10","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the American Mathematical Society, Series B","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/bproc/223","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We show that the characters of slr\mathfrak {sl}_r versions of the (1,p)(1,p) singlet and the (1,p)(1,p) triplet vertex operator algebras arise as limits of appropriately coloured slr\mathfrak {sl}_r Jones invariants of certain torus links.