The Poisson-Furstenberg kernel of a bounded symmetric domain
We study and give new informations about analysis and geometry in
bounded complex symmetric domains, using the theory of Jordan triple
systems. The main results are: an explicit description of the root
decomposition of the Lie algebra g of infinitesimal automorphisms;
a Jordan characterisation of the group N in the Iwasawa decomposition
G=KAN; description of horocycles; explicit formulas for
eigenfunctions of G-invariants operators and for the Poisson-Furstenberg
kernel, which is a reproducing kernel for G-harmonic functions.
F. Vandebrouck <vandebro@irma.u-strasbg.fr>