By James Arthur

A normal precept, chanced on through Robert Langlands and named by means of him the ''functoriality principle'' predicts family members among automorphic types on mathematics subgroups of alternative reductive teams. Langlands functoriality relates the eigenvalues of Hecke operators performing on the automorphic kinds on teams (or the neighborhood elements of the ''automorphic representations'' generated by means of them). within the few cases the place such kin were probed, they've got resulted in deep mathematics results. This publication stories one of many least difficult common difficulties within the concept, that of touching on automorphic kinds on mathematics subgroups of GL (n, E) and GL (n, F) while E/F is a cyclic extension of quantity fields. (This is named the bottom swap challenge for GL (n) the matter is attacked and solved via the hint formulation. The ebook depends upon deep and technical effects bought by means of a number of authors over the past two decades. it will probably no longer function an advent to them, yet, by way of giving whole references to the printed literature, the authors have made the paintings invaluable to a reader who doesn't understand the entire elements of the idea of automorphic kinds