Some results on simple supercuspidal representations of GL_n(F)

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• 作者：Moshe Adrian^a ; ¹ ; ^{moshe.adrian@qc.cuny.edu" class="auth_mail" title="E-mail the corresponding author} ; Baiying Liu^b ; ² ; ^{liu@math.utah.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：11S37 ; 22E50
• 刊名：Journal of Number Theory
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：160
• 期：Complete
• 页码：117-147
• 全文大小：559 K

文摘

Let F be a non-archimedean local field of characteristic zero with residual characteristic p  . In this paper, we first present a simple proof and construction of the local Langlands correspondence for simple supercuspidal representations of g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022314X1500270X&_mathId=si1.gif&_user=111111111&_pii=S0022314X1500270X&_rdoc=1&_issn=0022314X&md5=a6f4802ba13caa901d2b95b032b05d25" title="Click to view the MathML source">GL_n(F)gif" overflow="scroll">GLn(F), when g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022314X1500270X&_mathId=si2.gif&_user=111111111&_pii=S0022314X1500270X&_rdoc=1&_issn=0022314X&md5=b5568f4625fb9f80c2e31f00d70858fb" title="Click to view the MathML source">p∤ngif" overflow="scroll">p∤n. Our proof relies on the existence of the local Langlands correspondence for g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022314X1500270X&_mathId=si1.gif&_user=111111111&_pii=S0022314X1500270X&_rdoc=1&_issn=0022314X&md5=a6f4802ba13caa901d2b95b032b05d25" title="Click to view the MathML source">GL_n(F)gif" overflow="scroll">GLn(F), due to Harris/Taylor and Henniart. We then prove Jacquet's conjecture on the local converse problem for g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022314X1500270X&_mathId=si1.gif&_user=111111111&_pii=S0022314X1500270X&_rdoc=1&_issn=0022314X&md5=a6f4802ba13caa901d2b95b032b05d25" title="Click to view the MathML source">GL_n(F)gif" overflow="scroll">GLn(F) in the case of simple supercuspidal representations, following the strategy of Jiang, Nien and Stevens. Recently, Reeder and Yu constructed a family of epipelagic supercuspidal representations for semi-simple p  -adic groups. In the last part of our paper, we show that the analogous construction for g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022314X1500270X&_mathId=si1.gif&_user=111111111&_pii=S0022314X1500270X&_rdoc=1&_issn=0022314X&md5=a6f4802ba13caa901d2b95b032b05d25" title="Click to view the MathML source">GL_n(F)gif" overflow="scroll">GLn(F) produces only simple supercuspidals. In the process, we conclude that the constructed epipelagic supercuspidals of Reeder and Yu may not necessarily exhaust all epipelagic supercuspidals of a p-adic group.