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SUMMARY:Higher local constants\, local global principles and the Langlands
  correspondence for GL(n) - Guy Henniart (Paris-Sud)
DTSTART:20200122T163000Z
DTEND:20200122T173000Z
UID:TALK136591@talks.cam.ac.uk
CONTACT:Christopher Brookes
DESCRIPTION:Let F be a p-adic field. The local Langlands correspondence fo
 r GL(n\,F) relates irreducible degree n representations of the absolute G
 alois group of F to\ncuspidal representations of GL(n\,F). For n=1 it is g
 iven by class field theory\, and for n>1 it is characterized by the preser
 vation of fine invariants called "epsilon factors for pairs"\, obtained fr
 om the tensor product of two representations on the Galois side\, and by R
 ankin-Selberg convolutions on the GL(n) side. But there are other invarian
 ts defined on both sides\, and naturally they should correspond via the La
 nglands correspondence too.\n\nAfter a general introduction to the topic\,
  we shall look at the local factors which correspond on the Galois side to
  taking the exterior and symmetric square of a representation\, and are o
 btained on the GL(n) side by a method of Langlands-Shahidi.\n\nWe shall i
 ndicate a global-local proof of their preservation by the Langlands corres
 pondence\, which uses the Galois representations attached to\nregular alge
 braic cuspidal automorphic representations of GL(n) over (totally real) nu
 mber fields.\n 
LOCATION:MR12
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