n-Dimensional global correspondences of Langlands

Abstract

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.

143 pages

References in corpus (2)

• The non-commutative Weil algebra
• Algebraic representations of von Neumann algebras

Cited by in corpus (13)

• Algebraic quantum theory
• n-Dimensional global correspondences of Langlands over singular schemes (II)
• From global class field concepts and modular representations to the conjectures of Shimura-Taniyama-Weil,Birch-Swinnerton-Dyer and Riemann
• A new track for unifying general relativity with quantum field theories
• Algebraic representations of von Neumann algebras
• Higher algebraic K-theories related to the global program of Langlands
• The Langlands functoriality conjecture in the bisemialgebra framework
• Brane and string field structure of elementary particles
• n-Dimensional geometric-shifted global bilinear correspondences of Langlands on mixed motives III
• Random matrices and Riemann hypothesis
• Mass generation of elementary particles and origin of the fundamental forces in algebraic quantum theory
• The Thurston's program derived from the Langlands global program with singularities
• Generalized modular forms including the weak Maass forms,the Ramanujan's Theta functions and the Tau function