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

Abstract

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 Rankin–Cohen brackets (case $V=\mathbb{R}$).