F-method for constructing equivariant differential operators
  Using an algebraic Fourier transform of operators, we develop a method (F-method) to obtain explicit highest weight vectors in the branching laws by differential equations. This article gives a brief explanation of the F-method and its applications to a concrete construction of some natural equivariant operators that arise in parabolic geometry and in automorphic forms. 
Toshiyuki Kobayashi
math.RT math.DG