Conformally Covariant Bi-Differential Operators on a Simple Real Jordan Algebra

Abstract

For a simple real Jordan algebra $V,$ a family of bi-differential operators from ${\mathcal{C}}^{\infty }(V\times V)$ to ${\mathcal{C}}^{\infty }(V)$ is constructed. These operators are covariant under the rational action of the conformal group of $V.$ They generalize the classical {\em Rankin-Cohen} brackets (case $V=\mathbb{R}$).