Simple cuspidals and the local Langlands correspondence for GL(n)
Seminar Room 1, Newton Institute
Class field theory is the case n=1 of the Langlands correspondence. The case of general n may be considered as a kind of non-abelian class field theory. However the Langlands correspondence relates two equally mysterious sides. On the example of simple cuspidal representations for GL(n) over a non-Archimedean local field (pointed out by Gross and Reeder), we shall see that it is not so easy, but still possible, to determine the corresponding Galois representations (joint work in progress with Bushnell).