{"title":"a2 $A_2$ Rogers-Ramanujan三阶二分恒等式的一个例子","authors":"Shunsuke Tsuchioka","doi":"10.1112/jlms.70152","DOIUrl":null,"url":null,"abstract":"<p>We give manifestly positive Andrews–Gordon type series for the level 3 standard modules of the affine Lie algebra of type <span></span><math>\n <semantics>\n <msubsup>\n <mi>A</mi>\n <mn>2</mn>\n <mrow>\n <mo>(</mo>\n <mn>1</mn>\n <mo>)</mo>\n </mrow>\n </msubsup>\n <annotation>$A^{(1)}_2$</annotation>\n </semantics></math>. We also give corresponding bipartition identities, which have representation theoretic interpretations via the vertex operators. Our proof is based on the Borodin product formula, the Corteel–Welsh recursion for the cylindric partitions, a <span></span><math>\n <semantics>\n <mi>q</mi>\n <annotation>$q$</annotation>\n </semantics></math>-version of Sister Celine's technique and a generalization of Andrews' partition ideals by finite automata due to Takigiku and the author.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 4","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2025-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"An example of \\n \\n \\n A\\n 2\\n \\n $A_2$\\n Rogers–Ramanujan bipartition identities of level 3\",\"authors\":\"Shunsuke Tsuchioka\",\"doi\":\"10.1112/jlms.70152\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We give manifestly positive Andrews–Gordon type series for the level 3 standard modules of the affine Lie algebra of type <span></span><math>\\n <semantics>\\n <msubsup>\\n <mi>A</mi>\\n <mn>2</mn>\\n <mrow>\\n <mo>(</mo>\\n <mn>1</mn>\\n <mo>)</mo>\\n </mrow>\\n </msubsup>\\n <annotation>$A^{(1)}_2$</annotation>\\n </semantics></math>. We also give corresponding bipartition identities, which have representation theoretic interpretations via the vertex operators. Our proof is based on the Borodin product formula, the Corteel–Welsh recursion for the cylindric partitions, a <span></span><math>\\n <semantics>\\n <mi>q</mi>\\n <annotation>$q$</annotation>\\n </semantics></math>-version of Sister Celine's technique and a generalization of Andrews' partition ideals by finite automata due to Takigiku and the author.</p>\",\"PeriodicalId\":49989,\"journal\":{\"name\":\"Journal of the London Mathematical Society-Second Series\",\"volume\":\"111 4\",\"pages\":\"\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2025-04-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of the London Mathematical Society-Second Series\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/jlms.70152\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the London Mathematical Society-Second Series","FirstCategoryId":"100","ListUrlMain":"https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/jlms.70152","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
An example of
A
2
$A_2$
Rogers–Ramanujan bipartition identities of level 3
We give manifestly positive Andrews–Gordon type series for the level 3 standard modules of the affine Lie algebra of type . We also give corresponding bipartition identities, which have representation theoretic interpretations via the vertex operators. Our proof is based on the Borodin product formula, the Corteel–Welsh recursion for the cylindric partitions, a -version of Sister Celine's technique and a generalization of Andrews' partition ideals by finite automata due to Takigiku and the author.
期刊介绍：
The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
