{"title":"经典𝑝-adic组的Corank 3的单一性","authors":"Marko Tadić","doi":"10.1090/memo/1421","DOIUrl":null,"url":null,"abstract":"<p>Let <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G\">\n <mml:semantics>\n <mml:mi>G</mml:mi>\n <mml:annotation encoding=\"application/x-tex\">G</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula> be the <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper F\">\n <mml:semantics>\n <mml:mi>F</mml:mi>\n <mml:annotation encoding=\"application/x-tex\">F</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula>-points of a classical group defined over a <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"p\">\n <mml:semantics>\n <mml:mi>p</mml:mi>\n <mml:annotation encoding=\"application/x-tex\">p</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula>-adic field <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper F\">\n <mml:semantics>\n <mml:mi>F</mml:mi>\n <mml:annotation encoding=\"application/x-tex\">F</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula> of characteristic <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"0\">\n <mml:semantics>\n <mml:mn>0</mml:mn>\n <mml:annotation encoding=\"application/x-tex\">0</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula>. We classify the irreducible unitarizable representation of <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G\">\n <mml:semantics>\n <mml:mi>G</mml:mi>\n <mml:annotation encoding=\"application/x-tex\">G</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula> that are subquotients of the parabolic induction of cuspidal representations of Levi subgroup of corank at most 3 in <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G\">\n <mml:semantics>\n <mml:mi>G</mml:mi>\n <mml:annotation encoding=\"application/x-tex\">G</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula>.</p>","PeriodicalId":49828,"journal":{"name":"Memoirs of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":2.0000,"publicationDate":"2020-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"Unitarizability in Corank Three for Classical 𝑝-adic Groups\",\"authors\":\"Marko Tadić\",\"doi\":\"10.1090/memo/1421\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Let <inline-formula content-type=\\\"math/mathml\\\">\\n<mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"upper G\\\">\\n <mml:semantics>\\n <mml:mi>G</mml:mi>\\n <mml:annotation encoding=\\\"application/x-tex\\\">G</mml:annotation>\\n </mml:semantics>\\n</mml:math>\\n</inline-formula> be the <inline-formula content-type=\\\"math/mathml\\\">\\n<mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"upper F\\\">\\n <mml:semantics>\\n <mml:mi>F</mml:mi>\\n <mml:annotation encoding=\\\"application/x-tex\\\">F</mml:annotation>\\n </mml:semantics>\\n</mml:math>\\n</inline-formula>-points of a classical group defined over a <inline-formula content-type=\\\"math/mathml\\\">\\n<mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"p\\\">\\n <mml:semantics>\\n <mml:mi>p</mml:mi>\\n <mml:annotation encoding=\\\"application/x-tex\\\">p</mml:annotation>\\n </mml:semantics>\\n</mml:math>\\n</inline-formula>-adic field <inline-formula content-type=\\\"math/mathml\\\">\\n<mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"upper F\\\">\\n <mml:semantics>\\n <mml:mi>F</mml:mi>\\n <mml:annotation encoding=\\\"application/x-tex\\\">F</mml:annotation>\\n </mml:semantics>\\n</mml:math>\\n</inline-formula> of characteristic <inline-formula content-type=\\\"math/mathml\\\">\\n<mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"0\\\">\\n <mml:semantics>\\n <mml:mn>0</mml:mn>\\n <mml:annotation encoding=\\\"application/x-tex\\\">0</mml:annotation>\\n </mml:semantics>\\n</mml:math>\\n</inline-formula>. We classify the irreducible unitarizable representation of <inline-formula content-type=\\\"math/mathml\\\">\\n<mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"upper G\\\">\\n <mml:semantics>\\n <mml:mi>G</mml:mi>\\n <mml:annotation encoding=\\\"application/x-tex\\\">G</mml:annotation>\\n </mml:semantics>\\n</mml:math>\\n</inline-formula> that are subquotients of the parabolic induction of cuspidal representations of Levi subgroup of corank at most 3 in <inline-formula content-type=\\\"math/mathml\\\">\\n<mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"upper G\\\">\\n <mml:semantics>\\n <mml:mi>G</mml:mi>\\n <mml:annotation encoding=\\\"application/x-tex\\\">G</mml:annotation>\\n </mml:semantics>\\n</mml:math>\\n</inline-formula>.</p>\",\"PeriodicalId\":49828,\"journal\":{\"name\":\"Memoirs of the American Mathematical Society\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.0000,\"publicationDate\":\"2020-06-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Memoirs of the American Mathematical Society\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1090/memo/1421\",\"RegionNum\":4,\"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":"Memoirs of the American Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1090/memo/1421","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Unitarizability in Corank Three for Classical 𝑝-adic Groups
Let GG be the FF-points of a classical group defined over a pp-adic field FF of characteristic 00. We classify the irreducible unitarizable representation of GG that are subquotients of the parabolic induction of cuspidal representations of Levi subgroup of corank at most 3 in GG.
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Memoirs of the American Mathematical Society is devoted to the publication of research in all areas of pure and applied mathematics. The Memoirs is designed particularly to publish long papers or groups of cognate papers in book form, and is under the supervision of the Editorial Committee of the AMS journal Transactions of the AMS. To be accepted by the editorial board, manuscripts must be correct, new, and significant. Further, they must be well written and of interest to a substantial number of mathematicians.
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