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SUMMARY:Higher local constants\, local global principles\, and the Langlan
 ds correspondence for GL(n) - Guy Henniart (Université Paris-Sud)
DTSTART:20200122T163000Z
DTEND:20200122T173000Z
UID:TALK135355@talks.cam.ac.uk
CONTACT:Jessica Fintzen
DESCRIPTION:Let F be a p-adic field. The local Langlands correspondence fo
 r GL(n\,F)  relates\nirreducible degree n representations of the absolute 
 Galois group of F to cuspidal\nrepresentations of GL(n\,F). For n=1 it is 
 given by class field theory\, and for n>1\nit is characterized by the pres
 ervation of fine invariants called "epsilon factors for pairs"\,\nobtained
  from the tensor product of two representations on the Galois side\, and b
 y\nRankin-Selberg convolutions on the GL(n) side. But there are other inva
 riants defined\non both sides\, and naturally they should correspond via t
 he Langlands correspondence too.\n\nAfter a general introduction to the to
 pic\, we shall look at the local factors which\ncorrespond on the Galois s
 ide to taking the exterior and symmetric square of a\nrepresentation\, and
  are obtained on the GL(n) side by a method of Langlands-Shahidi.\n\nWe sh
 all indicate a global-local proof of their preservation\nby the Langlands 
 correspondence\, which uses the Galois representations attached to\nregula
 r algebraic cuspidal automorphic representations of GL(n) over\n(totally r
 eal) number fields.
LOCATION:MR12
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