{"title":"二级标准模块为A9(2)和Kanade-Russell划分条件","authors":"Kana Ito","doi":"10.1016/j.jalgebra.2024.11.031","DOIUrl":null,"url":null,"abstract":"<div><div>We give <em>Z</em>-monomial generators for the vacuum spaces of certain level 2 standard modules of type <span><math><msubsup><mrow><mi>A</mi></mrow><mrow><mtext>odd</mtext></mrow><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow></msubsup></math></span> with indices running over integer partitions. In particular, we give a Lie theoretic interpretation of the Rogers-Ramanujan type identities of type <span><math><msubsup><mrow><mi>A</mi></mrow><mrow><mn>9</mn></mrow><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow></msubsup></math></span>, which were conjectured by Kanade-Russell, and proven by Bringmann et al. and Rosengren.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"667 ","pages":"Pages 746-777"},"PeriodicalIF":0.8000,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Level 2 standard modules for A9(2) and partition conditions of Kanade-Russell\",\"authors\":\"Kana Ito\",\"doi\":\"10.1016/j.jalgebra.2024.11.031\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>We give <em>Z</em>-monomial generators for the vacuum spaces of certain level 2 standard modules of type <span><math><msubsup><mrow><mi>A</mi></mrow><mrow><mtext>odd</mtext></mrow><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow></msubsup></math></span> with indices running over integer partitions. In particular, we give a Lie theoretic interpretation of the Rogers-Ramanujan type identities of type <span><math><msubsup><mrow><mi>A</mi></mrow><mrow><mn>9</mn></mrow><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow></msubsup></math></span>, which were conjectured by Kanade-Russell, and proven by Bringmann et al. and Rosengren.</div></div>\",\"PeriodicalId\":14888,\"journal\":{\"name\":\"Journal of Algebra\",\"volume\":\"667 \",\"pages\":\"Pages 746-777\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2025-04-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Algebra\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S002186932400680X\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2025/1/3 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Algebra","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S002186932400680X","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2025/1/3 0:00:00","PubModel":"Epub","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
我们给出了指数在整数分区上运行的一类2级标准模的真空空间的z -单项式生成器。特别地，我们给出了由Kanade-Russell推测并由Bringmann et al.和Rosengren证明的A9(2)型的Rogers-Ramanujan型恒等式的李论解释。
Level 2 standard modules for A9(2) and partition conditions of Kanade-Russell
We give Z-monomial generators for the vacuum spaces of certain level 2 standard modules of type with indices running over integer partitions. In particular, we give a Lie theoretic interpretation of the Rogers-Ramanujan type identities of type , which were conjectured by Kanade-Russell, and proven by Bringmann et al. and Rosengren.
期刊介绍：
The Journal of Algebra is a leading international journal and publishes papers that demonstrate high quality research results in algebra and related computational aspects. Only the very best and most interesting papers are to be considered for publication in the journal. With this in mind, it is important that the contribution offer a substantial result that will have a lasting effect upon the field. The journal also seeks work that presents innovative techniques that offer promising results for future research.
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