  the program of Langlands is studied here on the basis of: a)new concepts of
global class field theory related to the explicit construction of global class
fields and of reciprocity laws; b)the representations of the reductive
algebraic groups GL(n) constituting the n-dimensional representations of the
associated global Weil groups; c)a toroidal compactification of the conjugacy
classes of these reductive algebraic groups whose analytic representations
constitute the cuspidal representations of these groups GL(n) in the context of
harmonic analysis. This leads us to build two types of n-dimensional global
bilinear correspondences of Langlands by taking into account the irreducibility
or the reducibility of the representations of the considered bilinear algebraic
semigroups. The major outcome of this global approach is the generation of
general algebraic symmetric structures, consisting of double symmetric towers
of conjugacy class representatives of algebraic groups,so that the analytic
toroidal representations of these conjugacy classes are the cuspidal conjugacy
class representatives of these bilinear algebraic semigroups.
