{"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.
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