2005/10/17 by Christian Pierre, Pierre, Christian · 3 citations
Mathematics · #11G18 #11R34 #11R37 #11R39 #Advanced Algebra and Geometry #Advanced Topics in Algebra #FOS: Mathematics #Geometry and complex manifolds #Representation Theory (math.RT) #math.RT #msc:11G18 #msc:11R34 #msc:11R37 #msc:11R39
paper · pdf · doi:10.48550/arxiv.math/0510348
143 pages
openalex publication_date 2005/10/17 · arxiv created 2009/11/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.