{"title":"关于ℚ𝑝上四元代数的一些𝑝和模𝑝表示","authors":"Yongquan Hu, Haoran Wang","doi":"10.1515/crelle-2024-0025","DOIUrl":null,"url":null,"abstract":"\n <jats:p>Let 𝐷 be the nonsplit quaternion algebra over <jats:inline-formula>\n <jats:alternatives>\n <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\n <m:msub>\n <m:mi mathvariant=\"double-struck\">Q</m:mi>\n <m:mi>p</m:mi>\n </m:msub>\n </m:math>\n <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_crelle-2024-0025_ineq_0001.png\"/>\n <jats:tex-math>\\mathbb{Q}_{p}</jats:tex-math>\n </jats:alternatives>\n </jats:inline-formula>.\nWe prove that a class of admissible unitary Banach space representations of <jats:inline-formula>\n <jats:alternatives>\n <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\n <m:msup>\n <m:mi>D</m:mi>\n <m:mo>×</m:mo>\n </m:msup>\n </m:math>\n <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_crelle-2024-0025_ineq_0002.png\"/>\n <jats:tex-math>D^{\\times}</jats:tex-math>\n </jats:alternatives>\n </jats:inline-formula> of global origin are topologically of finite length.</jats:p>","PeriodicalId":508691,"journal":{"name":"Journal für die reine und angewandte Mathematik (Crelles Journal)","volume":"10 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On some 𝑝-adic and mod 𝑝 representations of quaternion algebra over ℚ𝑝\",\"authors\":\"Yongquan Hu, Haoran Wang\",\"doi\":\"10.1515/crelle-2024-0025\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"\\n <jats:p>Let 𝐷 be the nonsplit quaternion algebra over <jats:inline-formula>\\n <jats:alternatives>\\n <m:math xmlns:m=\\\"http://www.w3.org/1998/Math/MathML\\\">\\n <m:msub>\\n <m:mi mathvariant=\\\"double-struck\\\">Q</m:mi>\\n <m:mi>p</m:mi>\\n </m:msub>\\n </m:math>\\n <jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" xlink:href=\\\"graphic/j_crelle-2024-0025_ineq_0001.png\\\"/>\\n <jats:tex-math>\\\\mathbb{Q}_{p}</jats:tex-math>\\n </jats:alternatives>\\n </jats:inline-formula>.\\nWe prove that a class of admissible unitary Banach space representations of <jats:inline-formula>\\n <jats:alternatives>\\n <m:math xmlns:m=\\\"http://www.w3.org/1998/Math/MathML\\\">\\n <m:msup>\\n <m:mi>D</m:mi>\\n <m:mo>×</m:mo>\\n </m:msup>\\n </m:math>\\n <jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" xlink:href=\\\"graphic/j_crelle-2024-0025_ineq_0002.png\\\"/>\\n <jats:tex-math>D^{\\\\times}</jats:tex-math>\\n </jats:alternatives>\\n </jats:inline-formula> of global origin are topologically of finite length.</jats:p>\",\"PeriodicalId\":508691,\"journal\":{\"name\":\"Journal für die reine und angewandte Mathematik (Crelles Journal)\",\"volume\":\"10 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-05-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal für die reine und angewandte Mathematik (Crelles Journal)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1515/crelle-2024-0025\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal für die reine und angewandte Mathematik (Crelles Journal)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/crelle-2024-0025","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
让 𝐷 是 Q p 上的非分裂四元数代数。我们证明，全局原点的 D × D^{\times} 的一类可容许的单元巴纳赫空间表示在拓扑上是有限长的。
On some 𝑝-adic and mod 𝑝 representations of quaternion algebra over ℚ𝑝
Let 𝐷 be the nonsplit quaternion algebra over Qp\mathbb{Q}_{p}.
We prove that a class of admissible unitary Banach space representations of D×D^{\times} of global origin are topologically of finite length.
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