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UID:9094@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20260526T140000
DTEND;TZID=Europe/Paris:20260526T150000
DTSTAMP:20260520T172128Z
URL:https://www.i2m.univ-amu.fr/evenements/tba-295/
SUMMARY:Juliette Coutens (I2M): A trace Paley-Wiener theorem for GL(n\, F)\
 \GL(n\, E)
DESCRIPTION:Juliette Coutens: \nThis talk is related to the relative Langla
 nds' program\, which aims to extend the classical Langlands' program to sp
 herical varieties. In the classical case\, a well-known trace Paley-Wiene
 r theorem was given by Bernstein\, Deligne and Kazhdan in 1986. It gives 
 a characterization of the functions\n\n\n\n\n\n\n\n\nπ ↦ Trace(π(f))
 \n\n\n\n\n\n\n\n\nwith G a reductive p-adic group\, and where π ranges ov
 er isomorphism classes of smooth irreducible representations of G and f is
  a smooth function with compact support on G.\n\nWe will explain how to ex
 tend this to a specific relative case. That is when E/F is a quadratic ext
 ension of p-adic fields\, our main result is a scalar Paley-Wiener theorem
  for relative Bessel distributions on GL(n\, F)\\GL(n\, E). These distribu
 tions are relative characters of the form\nπ ↦ I_π(f)\,\nwhere f i
 s a smooth function with compact support on GL(n\, E)\, and π ranges ove
 r GL(n\, F)-distinguished irreducible tempered representations. Those rel
 ative characters are constructed from a GL(n\, F)-invariant functional and
  a Whittaker functional. We will explain how by using the local Langlands 
 correspondence\, and the base-change from a unitary group\, the relative c
 haracters can be described as elements of the "generic" Bernstein center o
 f the quasi-split unitary group U(n).\n
CATEGORIES:Séminaire,AGLR,Représentations des Groupes Réductifs
LOCATION:I2M Luminy - TPR2\, Salle de Séminaire 304-306 (3ème étage)\, 1
 63 Avenue de Luminy\, Marseille\, 13009\, France
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=163 Avenue de Luminy\, Mars
 eille\, 13009\, France;X-APPLE-RADIUS=100;X-TITLE=I2M Luminy - TPR2\, Sall
 e de Séminaire 304-306 (3ème étage):geo:0,0
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DTSTART:20260329T030000
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