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SUMMARY:The nonabelian elliptic Fourier transform for unipotent representa
 tions of p-adic groups - Dan Ciubotaru (University of Oxford)
DTSTART:20161122T143000Z
DTEND:20161122T153000Z
UID:TALK67458@talks.cam.ac.uk
CONTACT:Jack Thorne
DESCRIPTION:In this talk\, I will consider two nonabelian Fourier transfor
 ms related to elliptic unipotent representations of semisimple p-adic grou
 ps. The elliptic representation theory concerns the study of characters mo
 dulo the proper parabolically induced ones. The unipotent category of repr
 esentations was defined by Lusztig and it can be thought of as being the s
 mallest subcategory of smooth representations that is closed under the for
 mation of L-packets and such that it contains the Iwahori representations.
  The first Fourier transform is defined on the p-adic group side in terms 
 of the pseudocoefficients of these representations and Lusztig's nonabelia
 n Fourier transform for characters of finite groups of Lie type. The secon
 d one is defined ``on the dual side'' in terms of the Langlands-Kazhdan-Lu
 sztig parameters for unipotent elliptic representations of a split p-adic 
 group.  I will present a conjectural relation between them\, and exemplify
  this conjecture in some cases that are known\, the most notable case bein
 g that of split special orthogonal groups\, by the work of Moeglin and Wal
 dspurger. I will also try to  explain the relevance of this picture to the
  verification of the properties of unipotent L-packets and to a geometric 
 interpretation of formal degrees of square integrable representations. The
  talk is based on joint work with Eric Opdam.
LOCATION:MR13
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