{"title":"准分裂经典群的简单超凸𝐿-Packets","authors":"Masao Oi","doi":"10.1090/memo/1483","DOIUrl":null,"url":null,"abstract":"<p>In this memoir, for quasi-split classical groups over <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 fields, we determine the <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper L\">\n <mml:semantics>\n <mml:mi>L</mml:mi>\n <mml:annotation encoding=\"application/x-tex\">L</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula>-packets consisting of simple supercuspidal representations and their corresponding <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper L\">\n <mml:semantics>\n <mml:mi>L</mml:mi>\n <mml:annotation encoding=\"application/x-tex\">L</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula>-parameters, under the assumption that <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> is not equal to <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"2\">\n <mml:semantics>\n <mml:mn>2</mml:mn>\n <mml:annotation encoding=\"application/x-tex\">2</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula>. The key is an explicit computation of characters of simple supercuspidal representations and the endoscopic character relation, which is a characterization of the local Langlands correspondence for quasi-split classical groups.</p>","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Simple Supercuspidal 𝐿-Packets of Quasi-Split Classical Groups\",\"authors\":\"Masao Oi\",\"doi\":\"10.1090/memo/1483\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this memoir, for quasi-split classical groups over <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 fields, we determine the <inline-formula content-type=\\\"math/mathml\\\">\\n<mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"upper L\\\">\\n <mml:semantics>\\n <mml:mi>L</mml:mi>\\n <mml:annotation encoding=\\\"application/x-tex\\\">L</mml:annotation>\\n </mml:semantics>\\n</mml:math>\\n</inline-formula>-packets consisting of simple supercuspidal representations and their corresponding <inline-formula content-type=\\\"math/mathml\\\">\\n<mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"upper L\\\">\\n <mml:semantics>\\n <mml:mi>L</mml:mi>\\n <mml:annotation encoding=\\\"application/x-tex\\\">L</mml:annotation>\\n </mml:semantics>\\n</mml:math>\\n</inline-formula>-parameters, under the assumption that <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> is not equal to <inline-formula content-type=\\\"math/mathml\\\">\\n<mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"2\\\">\\n <mml:semantics>\\n <mml:mn>2</mml:mn>\\n <mml:annotation encoding=\\\"application/x-tex\\\">2</mml:annotation>\\n </mml:semantics>\\n</mml:math>\\n</inline-formula>. The key is an explicit computation of characters of simple supercuspidal representations and the endoscopic character relation, which is a characterization of the local Langlands correspondence for quasi-split classical groups.</p>\",\"PeriodicalId\":2,\"journal\":{\"name\":\"ACS Applied Bio Materials\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.6000,\"publicationDate\":\"2024-05-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACS Applied Bio Materials\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1090/memo/1483\",\"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/1483","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}
引用次数: 0
摘要
在这篇回忆录中,对于 p p -adic 场上的准分裂经典群,我们在 p p 不等于 2 2 的假设下,确定了由简单超pidal 表示及其相应 L L -参数组成的 L L -包。关键在于对简单超pidal 表示的特征和内视特征关系的明确计算,而内视特征关系是对准分裂经典群的局部朗兰兹对应关系的描述。
Simple Supercuspidal 𝐿-Packets of Quasi-Split Classical Groups
In this memoir, for quasi-split classical groups over pp-adic fields, we determine the LL-packets consisting of simple supercuspidal representations and their corresponding LL-parameters, under the assumption that pp is not equal to 22. The key is an explicit computation of characters of simple supercuspidal representations and the endoscopic character relation, which is a characterization of the local Langlands correspondence for quasi-split classical groups.