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SUMMARY:Spectral transfer category of affine Hecke algebras - Opdam\, EM (
 Amsterdam)
DTSTART:20090622T103000Z
DTEND:20090622T113000Z
UID:TALK18860@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:We introduce a notion of a ``spectral transfer morphism'' betw
 een affine Hecke algebras. Such a spectral transfer morphism from H_1 to H
 _2 is not given by an algebra homomorphism from H_1 to H_2 but rather by a
  homomorphism from the center Z_2 of H_2 to the center Z_1 of H_1 which is
  required to be ``compatible'' in a certain way with the Harish-Chandra mu
 -functions on Z_1 and Z_2. The main property of such a transfer morphism i
 s that it induces a correspondence between the tempered spectra of H_1 and
  H_2 which respects the canonical spectral measures (``Plancherel measures
 '')\, up to a locally constant factor with values in the rational numbers.
  \n\nThe category of smooth unipotent representations of a connected split
  simple p-adic group of adjoint type G(F) is Morita equivalent to a direct
  sum R of affine Hecke algebras. It is a remarkable fact that R admits an 
 essentially unique ``spectral transfer morphism'' to the Iwahori-Matsumoto
  Hecke algebra of G. This fact offers a new perspective on Reeder's classi
 fication of unipotent characters for exceptional split groups which works 
 in the general case\, leading to an alternative approach to Lusztig's clas
 sification of unipotent characters of G(F). \n
LOCATION:Seminar Room 1\, Newton Institute
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