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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Spectral transfer category of affine Hecke algebra
 s - Opdam\, EM (Amsterdam)
DTSTART;TZID=Europe/London:20090622T113000
DTEND;TZID=Europe/London:20090622T123000
UID:TALK18860AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/18860
DESCRIPTION:We introduce a notion of a ``spectral transfer mor
 phism'' between affine Hecke algebras. Such a spec
 tral transfer morphism from H_1 to H_2 is not give
 n by an algebra homomorphism from H_1 to H_2 but r
 ather 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-Ch
 andra mu-functions on Z_1 and Z_2. The main proper
 ty of such a transfer morphism is that it induces 
 a correspondence between the tempered spectra of H
 _1 and H_2 which respects the canonical spectral m
 easures (``Plancherel measures'')\, up to a locall
 y constant factor with values in the rational numb
 ers. \n\nThe category of smooth unipotent represen
 tations of a connected split simple p-adic group o
 f adjoint type G(F) is Morita equivalent to a dire
 ct sum R of affine Hecke algebras. It is a remarka
 ble fact that R admits an essentially unique ``spe
 ctral transfer morphism'' to the Iwahori-Matsumoto
  Hecke algebra of G. This fact offers a new perspe
 ctive on Reeder's classification of unipotent char
 acters for exceptional split groups which works in
  the general case\, leading to an alternative appr
 oach to Lusztig's classification of unipotent char
 acters of G(F). \n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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