{"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":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"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\":2,\"journal\":{\"name\":\"ACS Applied Bio Materials\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.6000,\"publicationDate\":\"2020-06-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACS Applied Bio Materials\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1090/memo/1421\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATERIALS SCIENCE, BIOMATERIALS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1090/memo/1421","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","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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