On the non-unitary unramified dual for classical 𝑝–adic groups

Muić, Goran

doi:10.1090/S0002-9947-06-03894-3

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ISSN 1088-6850(online) ISSN 0002-9947(print)

On the non-unitary unramified dual for classical -adic groups

Author: Goran Muic
Journal: Trans. Amer. Math. Soc. 358 (2006), 4653-4687
MSC (2000): Primary 22E35, 22E50; Secondary 11F70
Posted: May 17, 2006
MathSciNet review: 2231392
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Abstract: In this paper we give a Zelevinsky type classification of unramified irreducible representations of split classical groups.

[B] Dubravka Ban, Parabolic induction and Jacquet modules of representations of 𝑂(2𝑛,𝐹), Glas. Mat. Ser. III 34(54) (1999), no. 2, 147–185. MR 1739616 (2001m:22033)
[BM1] Dan Barbasch and Allen Moy, Whittaker models with an Iwahori fixed vector, Representation theory and analysis on homogeneous spaces (New Brunswick, NJ, 1993), Contemp. Math., vol. 177, Amer. Math. Soc., Providence, RI, 1994, pp. 101–105. MR 1303602 (95j:22024), http://dx.doi.org/10.1090/conm/177/01917
[BM2] Dan Barbasch and Allen Moy, A unitarity criterion for 𝑝-adic groups, Invent. Math. 98 (1989), no. 1, 19–37. MR 1010153 (90m:22038), http://dx.doi.org/10.1007/BF01388842
[BM3] Dan Barbasch and Allen Moy, Reduction to real infinitesimal character in affine Hecke algebras, J. Amer. Math. Soc. 6 (1993), no. 3, 611–635. MR 1186959 (93k:22015), http://dx.doi.org/10.1090/S0894-0347-1993-1186959-0
[BZ1] I. N. Bernstein and A. V. Zelevinsky, Induced representations of reductive 𝔭-adic groups. I, Ann. Sci. École Norm. Sup. (4) 10 (1977), no. 4, 441–472. MR 0579172 (58 #28310)
[BZ2] I. N. Bernšteĭn and A. V. Zelevinskiĭ, Representations of the group 𝐺𝐿(𝑛,𝐹), where 𝐹 is a local non-Archimedean field, Uspehi Mat. Nauk 31 (1976), no. 3(189), 5–70 (Russian). MR 0425030 (54 #12988)
[Car] P. Cartier, Representations of 𝑝-adic groups: a survey, Automorphic forms, representations and 𝐿-functions (Proc. Sympos. Pure Math., Oregon State Univ., Corvallis, Ore., 1977), Part 1, Proc. Sympos. Pure Math., XXXIII, Amer. Math. Soc., Providence, R.I., 1979, pp. 111–155. MR 546593 (81e:22029)
[KL] David Kazhdan and George Lusztig, Proof of the Deligne-Langlands conjecture for Hecke algebras, Invent. Math. 87 (1987), no. 1, 153–215. MR 862716 (88d:11121), http://dx.doi.org/10.1007/BF01389157
[Ku] S. S. Kudla, On the Theta Correspondence (lectures at European School of Group Theory, Beilngries, 1996).
[M1] Goran Muić, Some results on square integrable representations; irreducibility of standard representations, Internat. Math. Res. Notices 14 (1998), 705–726. MR 1637097 (99f:22031), http://dx.doi.org/10.1155/S1073792898000427
[M2] Goran Muić, A proof of Casselman-Shahidi’s conjecture for quasi-split classical groups, Canad. Math. Bull. 44 (2001), no. 3, 298–312. MR 1847492 (2002f:22015), http://dx.doi.org/10.4153/CMB-2001-030-4
[M3] Goran Muić, On generic irreducible representations of 𝑆𝑝(𝑛,𝐹) and 𝑆𝑂(2𝑛+1,𝐹), Glas. Mat. Ser. III 33(53) (1998), no. 1, 19–31. MR 1652772 (2000j:22020)
[MSh] Goran Muić and Freydoon Shahidi, Irreducibility of standard representations for Iwahori-spherical representations, Math. Ann. 312 (1998), no. 1, 151–165. MR 1645956 (99g:22012), http://dx.doi.org/10.1007/s002080050216
[Moe] C. Mœglin, Sur la classification des séries discrètes des groupes classiques 𝑝-adiques: paramètres de Langlands et exhaustivité, J. Eur. Math. Soc. (JEMS) 4 (2002), no. 2, 143–200 (French, with English summary). MR 1913095 (2003g:22021), http://dx.doi.org/10.1007/s100970100033
[MT] Colette Mœglin and Marko Tadić, Construction of discrete series for classical 𝑝-adic groups, J. Amer. Math. Soc. 15 (2002), no. 3, 715–786 (electronic). MR 1896238 (2003g:22020), http://dx.doi.org/10.1090/S0894-0347-02-00389-2
[MVW] Colette Mœglin, Marie-France Vignéras, and Jean-Loup Waldspurger, Correspondances de Howe sur un corps 𝑝-adique, Lecture Notes in Mathematics, vol. 1291, Springer-Verlag, Berlin, 1987 (French). MR 1041060 (91f:11040)
[Ra] Stephen Rallis, Langlands’ functoriality and the Weil representation, Amer. J. Math. 104 (1982), no. 3, 469–515. MR 658543 (84c:10025), http://dx.doi.org/10.2307/2374151
[Sh1] Freydoon Shahidi, A proof of Langlands’ conjecture on Plancherel measures; complementary series for 𝑝-adic groups, Ann. of Math. (2) 132 (1990), no. 2, 273–330. MR 1070599 (91m:11095), http://dx.doi.org/10.2307/1971524
[Sh2] Freydoon Shahidi, Twisted endoscopy and reducibility of induced representations for 𝑝-adic groups, Duke Math. J. 66 (1992), no. 1, 1–41. MR 1159430 (93b:22034), http://dx.doi.org/10.1215/S0012-7094-92-06601-4
[T1] Marko Tadić, On reducibility of parabolic induction, Israel J. Math. 107 (1998), 29–91. MR 1658535 (2001d:22012), http://dx.doi.org/10.1007/BF02764004
[T2] Marko Tadić, Structure arising from induction and Jacquet modules of representations of classical 𝑝-adic groups, J. Algebra 177 (1995), no. 1, 1–33. MR 1356358 (97b:22023), http://dx.doi.org/10.1006/jabr.1995.1284
[T3] Marko Tadić, A family of square integrable representations of classical 𝑝-adic groups in the case of general half-integral reducibilities, Glas. Mat. Ser. III 37(57) (2002), no. 1, 21–57. MR 1918092 (2004a:22017)
[Ze] A. V. Zelevinsky, Induced representations of reductive 𝔭-adic groups. II. On irreducible representations of 𝔊𝔏(𝔫), Ann. Sci. École Norm. Sup. (4) 13 (1980), no. 2, 165–210. MR 584084 (83g:22012)

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