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CATEGORIES:Number Theory Seminar
SUMMARY:The nonabelian elliptic Fourier transform for unip
otent representations of p-adic groups - Dan Ciubo
taru (University of Oxford)
DTSTART;TZID=Europe/London:20161122T143000
DTEND;TZID=Europe/London:20161122T153000
UID:TALK67458AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/67458
DESCRIPTION:In this talk\, I will consider two nonabelian Four
ier transforms related to elliptic unipotent repre
sentations of semisimple p-adic groups. The ellipt
ic representation theory concerns the study of cha
racters modulo the proper parabolically induced on
es. The unipotent category of representations was
defined by Lusztig and it can be thought of as bei
ng the smallest subcategory of smooth representati
ons that is closed under the formation of L-packet
s and such that it contains the Iwahori representa
tions. The first Fourier transform is defined on t
he p-adic group side in terms of the pseudocoeffic
ients of these representations and Lusztig's nonab
elian Fourier transform for characters of finite g
roups of Lie type. The second one is defined ``on
the dual side'' in terms of the Langlands-Kazhdan-
Lusztig parameters for unipotent elliptic represen
tations of a split p-adic group. I will present a
conjectural relation between them\, and exemplify
this conjecture in some cases that are known\, th
e most notable case being that of split special or
thogonal groups\, by the work of Moeglin and Walds
purger. I will also try to explain the relevance
of this picture to the verification of the propert
ies of unipotent L-packets and to a geometric inte
rpretation of formal degrees of square integrable
representations. The talk is based on joint work w
ith Eric Opdam.
LOCATION:MR13
CONTACT:Jack Thorne
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