The purpose of this research is to give a dual description conformal blocks d=2 rational CFT (conformal field theory) in terms Hecke eigenforms and eigensheaves. In particular, partition functions, characters lattice theta functions may be reconstructed from the action operators. This method can applied to: 1) rings integers Galois number fields equipped with trace (or anti-trace) form; 2) root...

Abstract This survey reports on some of the recent developments in area Galois representations and automorphic forms, with a particular focus author Thorne’s work symmetric power functoriality for modular forms.

We establish a formula for the weight multiplicities of Demazure modules (in particular for highest weight representations) of a complex connected algebraic group in terms of the geometry of its Langlands dual.