The Hecke algebra of a reductive p-adic group: a geometric conjecture

  • Anne-Marie Aubert
  • Paul Baum
  • Roger Plymen
Part of the Aspects of Mathematics book series (ASMA)


Let H(G) be the Hecke algebra of a reductive p-adic group G. We formulate a conjecture for the ideals in the Bernstein decomposition of H(G). The conjecture says that each ideal is geometrically equivalent to an algebraic variety. Our conjecture is closely related to Lusztig’s conjecture on the asymptotic Hecke algebra. We prove our conjecture for SL(2) and GL(n). We also prove part (1) of the conjecture for the Iwahori ideals of the groups PGL(n) and SO(5). The conjecture, if true, leads to a parametrization of the smooth dual of G by the points in a complex affine locally algebraic variety.


Weyl Group Coxeter Group Local Unit Coordinate Ring Levi Subgroup 
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Copyright information

© Friedr. Vieweg & Sohn Verlag ∣ GWV Fachverlage GmbH, Wiesbaden 2006

Authors and Affiliations

  • Anne-Marie Aubert
    • 1
  • Paul Baum
    • 2
  • Roger Plymen
    • 3
  1. 1.Institut de Mathématiques de JussieuU.M.R. 7586 du C.N.R.S.ParisFrance
  2. 2.Mathematics DepartmentPennsylvania State UniversityUniversity ParkUSA
  3. 3.School of MathematicsManchester UniversityManchesterEngland

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