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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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