Harmonic analysis on line bundles over the exceptional domain E7(−25)/U(1)E6

Abstract

Let DVI be an exceptional domain of tube type and let Hν the associated generalized Hua operator. In this paper, we determine the explicit formula of the action of the group E7(−25) on DVI. We compute explicitly the value of the generalized Hua operator on DVI. Also, we characterized the Lp-range, 1 ≤ p < ∞ of the generalized Poisson transform on the Shilov boundary for the domain DVI. We prove that this range is a Hua–Hardy type spaces for functions satisfying a Hua system of differential equations.