skip to content

Mathematical Research at the University of Cambridge


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.

Further information


Jan 22nd 2020
16:30 to 17:30




Guy Henniart (Université Paris-Sud)


Number Theory Seminar