Hua operators on homogeneous line bundles over non-tube type bounded symmetric domains

Abstract

Let $\Omega =G/K$ be a bounded symmetric domain of non-compact type. In this paper the image of the Poisson transform on the degenerate principal series representations of G attached to the Shilov boundary of Ω is considered. We characterize the images in terms of the third-order Hua operators $U_{\nu }$ and $W_{\nu }$. When Ω is the exceptional domain of type V, we give the explicit formulas for the operators $U_{\nu }$ and $W_{\nu }$.