{"title":"对数顶点算子代数的字符和环状链路的彩色不变式","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":"{\"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}","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
摘要
我们证明了 s l r \mathfrak {sl}_r 版本的 ( 1 , p ) (1,p) 单顶算子和 ( 1 , p ) (1,p) 三顶算子代数的特征是作为某些环链的适当颜色 s l r \mathfrak {sl}_r 琼斯不变式的极限出现的。
Characters of logarithmic vertex operator algebras and coloured invariants of torus links
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.
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