Universal deformation formula for non-abelian group actions

Abstract: 

In this talk, I will explain how to generalize Rieffel's deformation formula for a class of symplectic exponential solvable Lie group actions. This is based on quantization technics for rank one symplectic hermitian symmetric spaces of non-compact type, in the case where the associated homogeneous space is of group-type. After a short explanation of the geometric setup (that forces us to consider such groups only), I will explain how wavelette-analysis and provides powerful tools to establish suitable estimates in this situation. In particular, an interesting generalization of the Calderon-Vaillancourt theorem will be proven.