Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

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

 
 

 

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


Author: Goran Muic
Journal: Trans. Amer. Math. Soc. 358 (2006), 4653-4687
MSC (2000): Primary 22E35, 22E50; Secondary 11F70
DOI: https://doi.org/10.1090/S0002-9947-06-03894-3
Published electronically: May 17, 2006
MathSciNet review: 2231392
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we give a Zelevinsky type classification of unramified irreducible representations of split classical groups.


References [Enhancements On Off] (What's this?)

  • [B] D. Ban, Parabolic induction and Jacquet modules of representations of $ O(2n, F)$, Glas. Mat. Ser III 34(54)(2) (1999), 147-185. MR 1739616 (2001m:22033)
  • [BM1] D. Barbasch, A. Moy, Whittaker models with an Iwahori fixed vector, Representation theory and analysis on homogenuos spaces (New Brunswick, NJ, 1993) Amer. Math. Soc., Providence, Rhode Island (1994), 101-105. MR 1303602 (95j:22024)
  • [BM2] D. Barbasch, A. Moy, A unitarity criterion for $ p$-adic groups, Invent. Math. 98 (1989), 19-37. MR 1010153 (90m:22038)
  • [BM3] D. Barbasch, A. Moy, Reduction to real infinitensimal character in affine Hecke algebras, Journal of A.M.S. 6 (1993), 611-635. MR 1186959 (93k:22015)
  • [BZ1] I. N. Bernstein, A. V. Zelevinsky, Induced representations of reductive $ p$-adic groups I, Ann. Sci. École Norm Sup. 10 (1977), 441-472. MR 0579172 (58:28310)
  • [BZ2] I. N. Bernstein, A. V. Zelevinsky, Representations of the group $ GL(n, F)$, where $ F$ is a local non-archimedean field, Uspekhi Mat. Nauk 31 (1976), 5-70. 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, vol. XXXIII, Proc. Sympos. Pure Math., Amer. Math. Soc., Providence, R.I, 1979, pp. 111-155. MR 0546593 (81e:22029)
  • [KL] D. Kazhdan, G. Lusztig, Proof of the Deligne-Langlands conjecture for Hecke algebras, Invent. Math. 87 (1987), 153-215. MR 0862716 (88d:11121)
  • [Ku] S. S. Kudla, On the Theta Correspondence (lectures at European School of Group Theory, Beilngries, 1996).
  • [M1] G. Muic, Some results on square integrable representations; Irreducibility of standard representations, Internat. Math. Res. Notices 14 (1998), 705-726. MR 1637097 (99f:22031)
  • [M2] G. Muic, A proof of Casselman-Shahidi's conjecture for quasi-split classical groups, Canad. Math. Bull. 44 (2001), 298-312. MR 1847492 (2002f:22015)
  • [M3] G. Muic, On generic irreducible representations for $ Sp(n, F)$ and $ SO(2n+1, F)$, Glas. Mat. Ser III 33(53) (1988), 19-31. MR 1652772 (2000j:22020)
  • [MSh] G. Muic, F. Shahidi, Irreducibility of standard representations for Iwahori-spherical representations, Math. Ann. 312 (1998), 151-165. MR 1645956 (99g:22012)
  • [Moe] C. Moeglin, Sur la classification des séries discrètes des groupes classiques p-adiques: paramètres de Langlands et exhaustivité, J. Eur. Math. Soc. (JEMS) J. Eur. Math. Soc. (JEMS) 4 (2002), 143-200. MR 1913095 (2003g:22021)
  • [MT] C. Moeglin, M. Tadic, Construction of discrete series for classical $ p$-adic groups, Amer. J. Math. Soc. 15 (2002), 715-786. MR 1896238 (2003g:22020)
  • [MVW] C. Moeglin, M.-F. Vignéras, J.-L. Waldspurger, Correspondence de Howe sur un corps $ p$-adique, Lecture Notes in Math. 1291, 1987. MR 1041060 (91f:11040)
  • [Ra] S. Rallis, Langland's functoriality and the Weil representation, Amer. J. Math. 104 (1982), 469-515. MR 0658543 (84c:10025)
  • [Sh1] F. Shahidi, A proof of Langland's conjecture on Plancherel measures; complementary series for p-adic groups, Ann. of Math. 132 (1990), 273-330. MR 1070599 (91m:11095)
  • [Sh2] F. Shahidi, Twisted endoscopy and reducibility of induced representations for p-adic groups, Duke Math. J. 66 (1992), 1-41. MR 1159430 (93b:22034)
  • [T1] M. Tadic, On reducibility of parabolic induction, Israel J. Math. 107 (1998), 29-91. MR 1658535 (2001d:22012)
  • [T2] M. Tadic, Structure arising from induction and Jacquet modules of representations of classical $ p$-adic groups, Journal of Algebra 177 (1995), 1-33. MR 1356358 (97b:22023)
  • [T3] M. Tadic, A familiy of square-integrable representations of classical $ p$-adic groups in the case of general half-integral reducibilities groups, Glas. Mat. Ser. III 37 (2002), 21-57. MR 1918092 (2004a:22017)
  • [Ze] A. V. Zelevinsky, Induced representations of reductive p-adic groups. On irreducible representations of $ GL(n)$, Ann. Sci. Ecole Norm. Sup. 13 (1980), 165-210. MR 0584084 (83g:22012)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 22E35, 22E50, 11F70

Retrieve articles in all journals with MSC (2000): 22E35, 22E50, 11F70


Additional Information

Goran Muic
Affiliation: Department of Mathematics, University of Zagreb, Bijenicka 30, 10000 Zagreb, Croatia
Email: gmuic@math.hr

DOI: https://doi.org/10.1090/S0002-9947-06-03894-3
Received by editor(s): April 6, 2004
Received by editor(s) in revised form: November 22, 2004
Published electronically: May 17, 2006
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society