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CATEGORIES:Algebra and Representation Theory Seminar
SUMMARY:Higher local constants\, local global principles a
nd the Langlands correspondence for GL(n) - Guy He
nniart (Paris-Sud)
DTSTART;TZID=Europe/London:20200122T163000
DTEND;TZID=Europe/London:20200122T173000
UID:TALK136591AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/136591
DESCRIPTION:Let F be a p-adic field. The local Langlands corre
spondence for GL(n\,F) relates irreducible degree
n representations of the absolute Galois group of
F to\ncuspidal representations of GL(n\,F). For n=
1 it is given by class field theory\, and for n>1
it is characterized by the preservation of fine in
variants called "epsilon factors for pairs"\, obta
ined from the tensor product of two representation
s on the Galois side\, and by Rankin-Selberg convo
lutions on the GL(n) side. But there are other inv
ariants defined on both sides\, and naturally they
should correspond via the Langlands correspondenc
e too.\n\nAfter a general introduction to the topi
c\, we shall look at the local factors which corre
spond on the Galois side to taking the exterior an
d symmetric square of a representation\, and are o
btained on the GL(n) side by a method of Langlands
-Shahidi.\n\nWe shall indicate a global-local proo
f of their preservation by the Langlands correspon
dence\, which uses the Galois representations atta
ched to\nregular algebraic cuspidal automorphic re
presentations of GL(n) over (totally real) number
fields.\n
LOCATION:MR12
CONTACT:Christopher Brookes
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