{"title":"有理切列尼克代数 Ht,c(S3,h)在正特征中的表示","authors":"Martina Balagović, Jordan Barnes","doi":"10.1016/j.jalgebra.2024.08.014","DOIUrl":null,"url":null,"abstract":"<div><p>We study the rational Cherednik algebra <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>t</mi><mo>,</mo><mi>c</mi></mrow></msub><mo>(</mo><msub><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>,</mo><mi>h</mi><mo>)</mo></math></span> of type <span><math><msub><mrow><mi>A</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> in positive characteristic <em>p</em>, and its irreducible category <span><math><mi>O</mi></math></span> representations <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>t</mi><mo>,</mo><mi>c</mi></mrow></msub><mo>(</mo><mi>τ</mi><mo>)</mo></math></span>. For every possible value of <span><math><mi>p</mi><mo>,</mo><mi>t</mi><mo>,</mo><mi>c</mi></math></span>, and <em>τ</em> we calculate the Hilbert polynomial and the character of <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>t</mi><mo>,</mo><mi>c</mi></mrow></msub><mo>(</mo><mi>τ</mi><mo>)</mo></math></span>, and give explicit generators of the maximal proper graded submodule of the Verma module.</p></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0021869324004691/pdfft?md5=05b5b7def2f1dc1cc017665e423dba06&pid=1-s2.0-S0021869324004691-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Representations of the rational Cherednik algebra Ht,c(S3,h) in positive characteristic\",\"authors\":\"Martina Balagović, Jordan Barnes\",\"doi\":\"10.1016/j.jalgebra.2024.08.014\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We study the rational Cherednik algebra <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>t</mi><mo>,</mo><mi>c</mi></mrow></msub><mo>(</mo><msub><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>,</mo><mi>h</mi><mo>)</mo></math></span> of type <span><math><msub><mrow><mi>A</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> in positive characteristic <em>p</em>, and its irreducible category <span><math><mi>O</mi></math></span> representations <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>t</mi><mo>,</mo><mi>c</mi></mrow></msub><mo>(</mo><mi>τ</mi><mo>)</mo></math></span>. For every possible value of <span><math><mi>p</mi><mo>,</mo><mi>t</mi><mo>,</mo><mi>c</mi></math></span>, and <em>τ</em> we calculate the Hilbert polynomial and the character of <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>t</mi><mo>,</mo><mi>c</mi></mrow></msub><mo>(</mo><mi>τ</mi><mo>)</mo></math></span>, and give explicit generators of the maximal proper graded submodule of the Verma module.</p></div>\",\"PeriodicalId\":14888,\"journal\":{\"name\":\"Journal of Algebra\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-08-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0021869324004691/pdfft?md5=05b5b7def2f1dc1cc017665e423dba06&pid=1-s2.0-S0021869324004691-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Algebra\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0021869324004691\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"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/S0021869324004691","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
我们研究正特征 p 的 A2 型有理切列尼克代数 Ht,c(S3,h)及其不可还原的 O 类表示 Lt,c(τ)。对于 p,t,c 和 τ 的每一个可能值，我们都计算了希尔伯特多项式和 Lt,c(τ)的性质，并给出了维尔马模块的最大适当分级子模块的明确生成器。
Representations of the rational Cherednik algebra Ht,c(S3,h) in positive characteristic
We study the rational Cherednik algebra of type in positive characteristic p, and its irreducible category representations . For every possible value of , and τ we calculate the Hilbert polynomial and the character of , and give explicit generators of the maximal proper graded submodule of the Verma module.
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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