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Isogenies of Hecke algebras and a Langlands correspondence for ramified principal series representations

Author: Mark Reeder
Journal: Represent. Theory 6 (2002), 101-126
MSC (2000): Primary 22E50
Published electronically: July 16, 2002
MathSciNet review: 1915088
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Abstract: This paper gives a Langlands classification of constituents of ramified principal series representations for split $p$-adic groups with connected center.

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  • [A] D. Alvis, Ratios of dual generic degrees of a finite Coxeter group, Proc. Amer. Math. Soc. 91 (1984), 532-536. MR 85i:20013
  • [B1] A. Borel, Admissible representations of a semisimple group over a local field with vectors fixed under an Iwahori subgroup, Invent. Math. 35 (1976), 133-159. MR 56:3196
  • [B2] -, Linear Algebraic Groups, Springer-Verlag, 1991. MR 92d:20001
  • [BGG] I.N. Bernstein, I.M. Gel'fand, I.S. Gel' fand, Schubert cells and cohomology of the spaces $G/P$, Russian Math. Surveys 28 (1973), 1-26.
  • [BK] C. Bushnell, P. Kutzko, Smooth representations of reductive $p$-adic groups: structure theory via types, Proc. London Math. Soc. 77 (1998), 582-634. MR 2000c:22014
  • [C] R. Carter, Finite groups of Lie type: Conjugacy classes and characters, Wiley, 1985. MR 87d:20060
  • [CG] N. Chriss, V. Ginzburg, Representation theory and complex geometry, Birkhäuser, 1997. MR 98i:22021
  • [DLP] C. De Concini, G. Lusztig, C. Procesi, Homology of the zero-set of a nilpotent vector field on a flag manifold, J. Amer. Math. Soc. 1 (1988), 15-34. MR 89f:14052
  • [IM] N. Iwahori and H. Matsumoto, On some Bruhat decomposition and the structure of the Hecke rings of the $p$-adic Chevalley groups, Inst. Hautes Études Sci. Publ. Math. 25 (1965), 5-48. MR 32:2486
  • [KL] D. Kazhdan, G. Lusztig, Proof of the Deligne-Langlands conjecture for Hecke algebras, Invent. Math. 87 (1987), 153-215. MR 88d:11121
  • [L1] G. Lusztig, Affine Hecke algebras and their graded version, J. Amer. Math. Soc. 2 (1989), 599-635. MR 90e:22028
  • [L2] -, Notes on Affine Hecke Algebras, preprint, 1999.
  • [M] L. Morris, Tamely ramified intertwining algebras, Invent. Math. 114 (1993), 1-54. MR 94g:22035
  • [Mac] I.G. Macdonald, Polynomial functors and wreath products, J. Pure and Appl. Algebra 18 (1980), 173-204. MR 83j:15023
  • [RR] A. Ram, J. Ramagge, Affine Hecke algebras, cyclotomic Hecke algebras and Clifford theory, preprint, 1999. MR 93m:22020
  • [R1] M. Reeder, $p$-adic Whittaker functions and vector bundles on flag manifolds, Compositio. Math. 85 (1994), 9-36. MR 93m:22020
  • [R2] -, Whittaker functions, prehomogeneous vector spaces and standard representations of $p$-adic groups, J. Reine. Angew. Math. 450 (1994), 83-121. MR 95g:22032
  • [R3] -, Nonstandard intertwining operators and the structure of unramified principal series representations, Forum. Math. 9 (1997), 457-516. MR 98j:22028
  • [Ro] A. Roche, Types and Hecke algebras for principal series representations of split reductive $p$-adic groups, Ann Sci. École Norm. Sup. 31 (1998), 361-413. MR 99d:22028
  • [Rod1] F. Rodier, Décomposition de la série principale des groupes réductifs $p$-adiques, Noncommutative harmonic analysis and Lie groups, vol. 880, Lecture Notes in Math., Springer, Berlin, New York, 1981. MR 83i:22029
  • [Rod2] -, Whittaker models for admissible representations of reductive $p$-adic split groups, Harmonic Analysis on Homogeneous Spaces, vol. XXVI, Proc. Symp. Pure Math., 1973. MR 50:7419
  • [Se] J.-P. Serre, Local Fields, Springer-Verlag, New York, Berlin, 1979. MR 82e:12016
  • [Sh] F. Shahidi, A proof of Langlands' conjecture on Plancherel measures; complementary series for $p$-adic groups, Ann. Math. 132 (1990), 273-330. MR 91m:11095
  • [Sp] T. Springer, Reductive Groups, Automorphic Forms, Representations and $L$-functions, vol. xxxiii, Proc. Symp. Pure Math., 1979. MR 80h:20062
  • [St] R. Steinberg, Torsion in reductive groups, Adv. Math. 15 (1975), 63-92. MR 50:7369

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Additional Information

Mark Reeder
Affiliation: Department of Mathematics, Boston College, Chestnut Hill, Massachusetts 02467

Received by editor(s): April 30, 2001
Received by editor(s) in revised form: January 30, 2002
Published electronically: July 16, 2002
Additional Notes: This work was partially supported by the National Science Foundation
Article copyright: © Copyright 2002 American Mathematical Society

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