{"title":"强实数形式上的 L 包","authors":"N. Arancibia Robert, P. Mezo","doi":"10.1090/ert/667","DOIUrl":null,"url":null,"abstract":"<p>Langlands [<italic>On the classification of irreducible representations of real algebraic groups</italic>, Math. Surveys Monogr., vol. 31, Amer. Math. Soc., Providence, RI, 1989, pp. 101–170] defined <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper L\"> <mml:semantics> <mml:mi>L</mml:mi> <mml:annotation encoding=\"application/x-tex\">L</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-packets for real reductive groups. In order to refine the local Langlands correspondence, Adams-Barbasch-Vogan [<italic>The Langlands classification and irreducible characters for real reductive groups</italic>, Progress in Mathematics, vol. 104, Birkhäuser Boston, Inc., Boston, MA, 1992] combined L-packets over all real forms belonging to an inner class. In the tempered setting, using different methods, Kaletha [Ann. of Math. (2) 184 (2016), pp. 559–632] also defines such combined L-packets with a refinement to the local Langlands correspondence. We prove that the tempered L-packets of Adams-Barbasch-Vogan and Kaletha are the same and are parameterized identically.</p>","PeriodicalId":51304,"journal":{"name":"Representation Theory","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2024-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"L-packets over strong real forms\",\"authors\":\"N. Arancibia Robert, P. Mezo\",\"doi\":\"10.1090/ert/667\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Langlands [<italic>On the classification of irreducible representations of real algebraic groups</italic>, Math. Surveys Monogr., vol. 31, Amer. Math. Soc., Providence, RI, 1989, pp. 101–170] defined <inline-formula content-type=\\\"math/mathml\\\"> <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"upper L\\\"> <mml:semantics> <mml:mi>L</mml:mi> <mml:annotation encoding=\\\"application/x-tex\\\">L</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-packets for real reductive groups. In order to refine the local Langlands correspondence, Adams-Barbasch-Vogan [<italic>The Langlands classification and irreducible characters for real reductive groups</italic>, Progress in Mathematics, vol. 104, Birkhäuser Boston, Inc., Boston, MA, 1992] combined L-packets over all real forms belonging to an inner class. In the tempered setting, using different methods, Kaletha [Ann. of Math. (2) 184 (2016), pp. 559–632] also defines such combined L-packets with a refinement to the local Langlands correspondence. We prove that the tempered L-packets of Adams-Barbasch-Vogan and Kaletha are the same and are parameterized identically.</p>\",\"PeriodicalId\":51304,\"journal\":{\"name\":\"Representation Theory\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2024-01-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Representation Theory\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1090/ert/667\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Representation Theory","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1090/ert/667","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
Langlands [On the classification of irreducible representations of real algebraic groups, Math.Surveys Monogr.Math.Soc., Providence, RI, 1989, pp.为了完善局部朗兰兹对应关系，亚当斯-巴尔巴什-沃根 [The Langlands classification and irreducible characters for real reductive groups, Progress in Mathematics, vol. 104, Birkhäuser Boston, Inc.在回火设置中，卡莱塔[Ann. of Math. (2) 184 (2016), pp.我们证明，Adams-Barbasch-Vogan 和 Kaletha 的回火 L-packets 是相同的，并且参数相同。
Langlands [On the classification of irreducible representations of real algebraic groups, Math. Surveys Monogr., vol. 31, Amer. Math. Soc., Providence, RI, 1989, pp. 101–170] defined LL-packets for real reductive groups. In order to refine the local Langlands correspondence, Adams-Barbasch-Vogan [The Langlands classification and irreducible characters for real reductive groups, Progress in Mathematics, vol. 104, Birkhäuser Boston, Inc., Boston, MA, 1992] combined L-packets over all real forms belonging to an inner class. In the tempered setting, using different methods, Kaletha [Ann. of Math. (2) 184 (2016), pp. 559–632] also defines such combined L-packets with a refinement to the local Langlands correspondence. We prove that the tempered L-packets of Adams-Barbasch-Vogan and Kaletha are the same and are parameterized identically.
期刊介绍：
All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are.
This electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content.
Representation Theory is an open access journal freely available to all readers and with no publishing fees for authors.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
