Tempered representations for classical p-adic groups
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| Vydané v: | Manuscripta mathematica Ročník 145; číslo 3-4; s. 319 - 387 |
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01.11.2014
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| Author | Jantzen, Chris |
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| Author_xml | – sequence: 1 givenname: Chris surname: Jantzen fullname: Jantzen, Chris email: jantzenc@ecu.edu organization: Department of Mathematics, East Carolina University |
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| Cites_doi | 10.2307/1971524 10.2307/2374942 10.1090/S1088-4165-07-00316-0 10.1090/S0894-0347-02-00389-2 10.1007/BF02786631 10.1006/jabr.1995.1284 10.1007/BFb0087916 10.4153/CJM-2005-025-4 10.1007/s100970100033 10.1142/9789812562500_0004 10.24033/asens.1333 10.4153/CJM-1995-019-8 10.2140/pjm.1993.161.347 10.1215/S0012-7094-92-06601-4 10.24033/asens.1379 10.1007/s00229-010-0423-8 10.1353/ajm.1997.0039 10.2307/121049 10.2307/1971110 10.1007/BF02764004 10.1016/S0012-9593(97)89916-8 10.4153/CJM-2005-007-x 10.1090/S0002-9947-06-03894-3 10.1090/S1088-4165-03-00166-3 10.1090/S1088-4165-00-00081-9 10.1007/BF02699536 10.1093/imrn/rnp128 10.4153/CJM-2011-003-2 10.1017/S1474748003000082 10.1515/crll.1999.050 |
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| References | MœglinC.Sur la classification des séries discrètes des groupes classiques; paramètres de Langlands et exhaustivitéJ. Eur. Math. Soc.2002414320010.1007/s1009701000331002.22009 MuićG.Composition series of generalized principal series; the case of strongly positive discrete seriesIsr. J. Math.200414015720210.1007/BF027866311055.22015 Tadić, M.: On classification of some classes of irreducible representations of classical groups. Representations of real and p-adic groups In: Tan, E.-C., Zhu, C.-B. (eds.) Lecture Notes Series. Institute of Mathematical Science, National University of Singapore, vol. 2. Singapore University Press, Singapore, pp. 95–162 (2004) GoldbergD.Reducibility for non-connected p-adic groups with G0 of prime indexCan. J. Math.19954734436310.4153/CJM-1995-019-80835.22015 GoldbergD.HerbR.Some results on the admissible representations of non-connected reductive p-adic groupsAnn. Sci. École Norm. Sup.1997309714614223140874.22016 ShahidiF.A proof of Langlands conjecture on Plancherel measure; complementary series for p-adic groupsAnn. Math.1990132273330107059910.2307/19715240780.22005 HerbR.Elliptic representations for Sp(2n) and SO(n)Pac. J. Math.1993161347358124220310.2140/pjm.1993.161.347 SchneiderP.StuhlerU.Representation theory and sheaves on the Bruhat–Tits buildingPubl. Math. IHES19978597191147186710.1007/BF026995360892.22012 MœglinC.Normalisation des opérateurs d’entrelacement et réductibilité des induites des cuspidales; le cas des groupes classiques p-adiquesAnn. Math.200015181784710.2307/1210490956.22012 Tadić, M.: On tempered and square integrable representations of classical p-adic groups. Preprint WaldspurgerJ.-L.La formule de Plancherel pour les groupes p-adiques d’après Harish-ChandraJ. Inst. Math. Jussieu20032235333198969310.1017/S14747480030000821029.22016 Casselman, W.: Introduction to the theory of admissible representations of p-adic reductive groups. Preprint. Available online at http://www.math.ubc.ca/people/faculty/cass/research.html as “The p-adic notes” JantzenC.On supports of induced representations for symplectic and odd-orthogonal groupsAm. J. Math.199711912131262148181410.1353/ajm.1997.00390888.22013 BanD.JantzenC.Degenerate principal series for even orthogonal groupsRepresent. Theory20037440480201706510.1090/S1088-4165-03-00166-31054.22015 BernsteinI.ZelevinskyA.Induced representations of reductive p-adic groups IAnn. Sci. École Norm. Sup.1977104414725791720412.22015 JantzenC.Jacquet modules of p-adic general linear groupsRepresent. Theory2007114583230660610.1090/S1088-4165-07-00316-01139.22014 GoldbergD.R-Groups and elliptic representations for unitary groupsProc. Am. Math. Soc.1995123126712760856.22023 ShahidiF.Twisted endoscopy and reducibility of induced representations for p-adic groupsDuke Math. J.199266141115943010.1215/S0012-7094-92-06601-40785.22022 GoldbergD.Reducibility of induced representations for Sp(2n) and SO(n)Am. J. Math.19941161101115110.2307/23749420851.22021 TadićM.On reducibility of parabolic inductionIsr. J. Math.1998107299110.1007/BF027640040914.22019 TadićM.On invariants of discrete series representations of classical p-adic groupsMauscripta Math.201113541743510.1007/s00229-010-0423-81222.22016 ZhangY.L-Packets and reducibilitiesJ. reine angew. Math.19995108310216960920918.22010 JantzenC.Square-integrable representations for symplectic and odd-orthogonal groups IIRepresent. Theory20004127180178946410.1090/S1088-4165-00-00081-91045.22018 JantzenC.Discrete series for p-adic SO(2n) and restrictions of representations of O(2n)Can. J. Math.201163327380280905910.4153/CJM-2011-003-21219.22016 SilbergerA.Special representations of reductive p-adic groups are not integrableAnn. Math.198011157158757713810.2307/19711100437.22015 Jacquet, H.: Generic representations. Non-commutative harmonic analysis (Actes Colloq., Marseille-Luminy, 1976). Lecture Notes in Mathematics, vol. 587, pp. 91–101. Springer, Berlin (1977) TadićM.Structure arising from induction and Jacquet modules of representations of classical p-adic groupsJ. Algebra1995177133135635810.1006/jabr.1995.12840874.22014 JantzenC.Duality and supports of induced representations for orthogonal groupsCan. J. Math.200557159179211385310.4153/CJM-2005-007-x1065.22013 MœglinC.TadićM.Construction of discrete series for classical p-adic groupsJ. Am. Math. Soc.20021571578610.1090/S0894-0347-02-00389-20992.22015 BanD.Parabolic induction and Jacquet modules of representations of O(2n,F)Glas. Mat.1999345414718517396160954.22013 MuićG.On the non-unitary unramified dual for classical p-adic groupsTrans. Am. Math. Soc.20063584653468710.1090/S0002-9947-06-03894-31102.22014 Aubert, A.-M.: Dualité dans le groupe de Grothendieck de la catégorie des représentations lisses de longueur finie d’un groupe réductif p-adique. Trans. Am. Math. Soc. 347(1995), 2179–2189 and Erratum: Trans. Amer. Math. Soc. 348, 4687–4690 (1996) ZelevinskyA.Induced representations of reductive p-adic groups II, On irreducible representations of GL(n)Ann. Sci. École Norm. Sup.1980131652105840840441.22014 JantzenC.Degenerate principal series for symplectic and odd-orthogonal groupsMem. Am. Math. Soc.199659011001346929 MœglinC.WaldspurgerJ.-L.Sur l’involution de ZelevinskiJ. reine angew. Math.19863721361778635220594.22008 MuićG.Reducibility of generalized principal seriesCan. J. Math.20055761664710.4153/CJM-2005-025-41068.22017 HanzerM.The generalized injectivity conjecture for classical p-adic groupsInt. Math. Res. Not.201021952372581039 679_CR1 R. Herb (679_CR11) 1993; 161 C. Jantzen (679_CR17) 2007; 11 679_CR32 M. Hanzer (679_CR10) 2010; 2 679_CR12 C. Jantzen (679_CR16) 2005; 57 679_CR34 679_CR5 G. Muić (679_CR24) 2005; 57 C. Mœglin (679_CR19) 2000; 151 A. Silberger (679_CR29) 1980; 111 G. Muić (679_CR23) 2004; 140 C. Jantzen (679_CR15) 2000; 4 M. Tadić (679_CR31) 1998; 107 M. Tadić (679_CR33) 2011; 135 C. Jantzen (679_CR13) 1996; 590 F. Shahidi (679_CR27) 1990; 132 D. Goldberg (679_CR7) 1995; 47 C. Jantzen (679_CR18) 2011; 63 D. Ban (679_CR3) 2003; 7 I. Bernstein (679_CR4) 1977; 10 G. Muić (679_CR25) 2006; 358 P. Schneider (679_CR26) 1997; 85 M. Tadić (679_CR30) 1995; 177 C. Jantzen (679_CR14) 1997; 119 D. Ban (679_CR2) 1999; 34 C. Mœglin (679_CR20) 2002; 4 C. Mœglin (679_CR21) 2002; 15 A. Zelevinsky (679_CR36) 1980; 13 F. Shahidi (679_CR28) 1992; 66 D. Goldberg (679_CR6) 1994; 116 D. Goldberg (679_CR9) 1997; 30 C. Mœglin (679_CR22) 1986; 372 Y. Zhang (679_CR37) 1999; 510 D. Goldberg (679_CR8) 1995; 123 J.-L. Waldspurger (679_CR35) 2003; 2 |
| References_xml | – reference: JantzenC.Duality and supports of induced representations for orthogonal groupsCan. J. Math.200557159179211385310.4153/CJM-2005-007-x1065.22013 – reference: GoldbergD.HerbR.Some results on the admissible representations of non-connected reductive p-adic groupsAnn. Sci. École Norm. Sup.1997309714614223140874.22016 – reference: Tadić, M.: On tempered and square integrable representations of classical p-adic groups. Preprint – reference: JantzenC.On supports of induced representations for symplectic and odd-orthogonal groupsAm. J. Math.199711912131262148181410.1353/ajm.1997.00390888.22013 – reference: ShahidiF.Twisted endoscopy and reducibility of induced representations for p-adic groupsDuke Math. J.199266141115943010.1215/S0012-7094-92-06601-40785.22022 – reference: Casselman, W.: Introduction to the theory of admissible representations of p-adic reductive groups. Preprint. Available online at http://www.math.ubc.ca/people/faculty/cass/research.html as “The p-adic notes” – reference: TadićM.Structure arising from induction and Jacquet modules of representations of classical p-adic groupsJ. Algebra1995177133135635810.1006/jabr.1995.12840874.22014 – reference: GoldbergD.Reducibility of induced representations for Sp(2n) and SO(n)Am. J. Math.19941161101115110.2307/23749420851.22021 – reference: MœglinC.Sur la classification des séries discrètes des groupes classiques; paramètres de Langlands et exhaustivitéJ. Eur. Math. Soc.2002414320010.1007/s1009701000331002.22009 – reference: Jacquet, H.: Generic representations. Non-commutative harmonic analysis (Actes Colloq., Marseille-Luminy, 1976). Lecture Notes in Mathematics, vol. 587, pp. 91–101. Springer, Berlin (1977) – reference: SilbergerA.Special representations of reductive p-adic groups are not integrableAnn. Math.198011157158757713810.2307/19711100437.22015 – reference: MœglinC.WaldspurgerJ.-L.Sur l’involution de ZelevinskiJ. reine angew. Math.19863721361778635220594.22008 – reference: GoldbergD.R-Groups and elliptic representations for unitary groupsProc. Am. Math. Soc.1995123126712760856.22023 – reference: JantzenC.Jacquet modules of p-adic general linear groupsRepresent. Theory2007114583230660610.1090/S1088-4165-07-00316-01139.22014 – reference: BanD.Parabolic induction and Jacquet modules of representations of O(2n,F)Glas. Mat.1999345414718517396160954.22013 – reference: MœglinC.Normalisation des opérateurs d’entrelacement et réductibilité des induites des cuspidales; le cas des groupes classiques p-adiquesAnn. Math.200015181784710.2307/1210490956.22012 – reference: MuićG.On the non-unitary unramified dual for classical p-adic groupsTrans. Am. Math. Soc.20063584653468710.1090/S0002-9947-06-03894-31102.22014 – reference: SchneiderP.StuhlerU.Representation theory and sheaves on the Bruhat–Tits buildingPubl. Math. IHES19978597191147186710.1007/BF026995360892.22012 – reference: Tadić, M.: On classification of some classes of irreducible representations of classical groups. Representations of real and p-adic groups In: Tan, E.-C., Zhu, C.-B. (eds.) Lecture Notes Series. Institute of Mathematical Science, National University of Singapore, vol. 2. Singapore University Press, Singapore, pp. 95–162 (2004) – reference: Aubert, A.-M.: Dualité dans le groupe de Grothendieck de la catégorie des représentations lisses de longueur finie d’un groupe réductif p-adique. Trans. Am. Math. Soc. 347(1995), 2179–2189 and Erratum: Trans. Amer. Math. Soc. 348, 4687–4690 (1996) – reference: TadićM.On reducibility of parabolic inductionIsr. J. Math.1998107299110.1007/BF027640040914.22019 – reference: ZhangY.L-Packets and reducibilitiesJ. reine angew. Math.19995108310216960920918.22010 – reference: ShahidiF.A proof of Langlands conjecture on Plancherel measure; complementary series for p-adic groupsAnn. Math.1990132273330107059910.2307/19715240780.22005 – reference: BernsteinI.ZelevinskyA.Induced representations of reductive p-adic groups IAnn. Sci. École Norm. Sup.1977104414725791720412.22015 – reference: GoldbergD.Reducibility for non-connected p-adic groups with G0 of prime indexCan. J. Math.19954734436310.4153/CJM-1995-019-80835.22015 – reference: HanzerM.The generalized injectivity conjecture for classical p-adic groupsInt. Math. Res. Not.201021952372581039 – reference: BanD.JantzenC.Degenerate principal series for even orthogonal groupsRepresent. Theory20037440480201706510.1090/S1088-4165-03-00166-31054.22015 – reference: MuićG.Reducibility of generalized principal seriesCan. J. Math.20055761664710.4153/CJM-2005-025-41068.22017 – reference: JantzenC.Discrete series for p-adic SO(2n) and restrictions of representations of O(2n)Can. J. Math.201163327380280905910.4153/CJM-2011-003-21219.22016 – reference: ZelevinskyA.Induced representations of reductive p-adic groups II, On irreducible representations of GL(n)Ann. Sci. École Norm. Sup.1980131652105840840441.22014 – reference: JantzenC.Square-integrable representations for symplectic and odd-orthogonal groups IIRepresent. Theory20004127180178946410.1090/S1088-4165-00-00081-91045.22018 – reference: HerbR.Elliptic representations for Sp(2n) and SO(n)Pac. J. Math.1993161347358124220310.2140/pjm.1993.161.347 – reference: WaldspurgerJ.-L.La formule de Plancherel pour les groupes p-adiques d’après Harish-ChandraJ. Inst. Math. Jussieu20032235333198969310.1017/S14747480030000821029.22016 – reference: TadićM.On invariants of discrete series representations of classical p-adic groupsMauscripta Math.201113541743510.1007/s00229-010-0423-81222.22016 – reference: JantzenC.Degenerate principal series for symplectic and odd-orthogonal groupsMem. Am. Math. Soc.199659011001346929 – reference: MœglinC.TadićM.Construction of discrete series for classical p-adic groupsJ. Am. Math. Soc.20021571578610.1090/S0894-0347-02-00389-20992.22015 – reference: MuićG.Composition series of generalized principal series; the case of strongly positive discrete seriesIsr. J. Math.200414015720210.1007/BF027866311055.22015 – volume: 132 start-page: 273 year: 1990 ident: 679_CR27 publication-title: Ann. Math. doi: 10.2307/1971524 – volume: 116 start-page: 1101 year: 1994 ident: 679_CR6 publication-title: Am. J. Math. doi: 10.2307/2374942 – volume: 123 start-page: 1267 year: 1995 ident: 679_CR8 publication-title: Proc. Am. Math. 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| SubjectTerms | Algebraic Geometry Calculus of Variations and Optimal Control; Optimization Geometry Lie Groups Mathematics Mathematics and Statistics Number Theory Topological Groups |
| Title | Tempered representations for classical p-adic groups |
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