p-adic典型群上轨道积分的若干性质-论文.pdf

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1、第32卷第2期江苏师范大学学报(自然科学版)V01．32，No．22014年6月JournalofJiangsuNormalUniversity(NaturalScienceEdition)Jun．，2014ArticleID：2095-4298(2014)02—0023—03Somepropertiesoforbitintegrals-●l●l0nlr-adtcclassicalRroupsYuXiaoxiang(SchoolofMathematics&Statistics，JiangsuNorma

2、lUniversity，Xuzhou221116，Jiangsu，China)Abstract：Somebasicpropertiesoforbitintegralsrelatedtoharmonicanalysisonp-adicclassicalgroupsarestudied，aformatofRieszrepresentationtheoryisproved，andcertaininvariantbehaviouroftheseorbitintegralsisil'lustra—ted．Key

3、words：classicalgroup；orbitintegral；representationtheorem；invariantmeasureCLCnumber：O156Documentcode：Adoi：10．3969／j．issn．2095—4298．2014．02．005p-adic典型群上轨道积分的若干性质俞小祥(江苏师范大学数学与统计学院，江苏徐州221116)摘要：研究了p-adic典型群上调和分析中轨道积分的一些基本属性，证明了轨道积分中的里兹表示定理，验证了它们的不变性．关键词：典

4、型群；轨道积分；表示定理；不变测度0IntroductionThestudyofintertwiningoperatorsplaysanimportantroleinLanglandsprogramandharmonicanaly—sis，itisraisedfromthestudyofEisensteinseries[卜。]andEisensteinintegrals[一．Recentbreakthroughtostudythoseoperatorsattachedtonon—genericsupe

5、rcuspidalrepresentationsistostudytheorbitinte—gralsassociatedtothem[。一，sincetheseintegralsdon’trequiretobearaWhittakermodel，bydoingso，onemayrelatetheharmonicanalysisonnon—genericrepresentationstogenericones．Asthetheoriesonge—nericrepresentations[’川arefa

6、irlywellknown，thiswillfindawaytoapproachthelocalLanglandspro—gram．Tosavecontext，we’11freelyusenotationsfromE6-8]，particularlyfromthoseinE9—11]．Howev—er，wearenottryingtoexposethewholeframeworkmentionedabove，butrather，onlydemonstratesomeelementaryandinter

7、estingpropertiesoftheseorbitintegrals．SupposeFisap-adicfield，letGfbeaquasi—splitconnectedreductiveclassicalgroupofrankldefinedoverF．LetM=GL(F)XGbetheLevisubgroupofamaximalparabolicsubgroupPofGt，whereGisasubgroupofthesametypeofG，withrankrn(Z一+m)．Letrandr

8、beunitaryirreduciblesupercuspi—dalrepresentationsofGL(F)andGm，respectively，withrbeingramified．Thenthevalueof(，A(s，．ctr，wo)^(P))ats一0isproportionaltO[)。()。吉g))(h-1)duodhdg．(1)∑aU。e∈AHerehisafunctionwhichliesintheinductionspaceInd)