Higher local constants, local global principles, and the Langlands correspondence for GL(n)

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• Guy Henniart (Université Paris-Sud)
• Wednesday 22 January 2020, 16:30-17:30
• MR12.

If you have a question about this talk, please contact Jessica Fintzen.

Let F be a p-adic field. The local Langlands correspondence for GL(n,F) relates irreducible degree n representations of the absolute Galois group of F to cuspidal 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 invariants called “epsilon factors for pairs”, obtained from the tensor product of two representations on the Galois side, and by Rankin-Selberg convolutions on the GL(n) side. But there are other invariants defined on both sides, and naturally they should correspond via the Langlands correspondence too.

After 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 obtained on the GL(n) side by a method of Langlands-Shahidi.

We shall indicate a global-local proof of their preservation by the Langlands correspondence, which uses the Galois representations attached to regular algebraic cuspidal automorphic representations of GL(n) over (totally real) number fields.

This talk is part of the Number Theory Seminar series.

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