{"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":49828,"journal":{"name":"Memoirs of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":2.0000,"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\":49828,\"journal\":{\"name\":\"Memoirs of the American Mathematical Society\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.0000,\"publicationDate\":\"2024-05-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Memoirs of the American Mathematical Society\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1090/memo/1483\",\"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/1483","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","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.
期刊介绍:
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.