Abstract
Let G be a connected noncompact semisimple group with finite center. Fix G = KAN an Iwasawa decomposition of G. That is, K is a maximal compact subgroup of G, A a maximal vector subgroup of G with Ad A consisting of semisimple elements normalizing N, a maximal simply connected nilpotent subgroup of G. The space 52 = G/K is a Riemannian symmetric space, and if M is the centralizer of A in K the group B = MAN is a minimal parabolic subgroup of G, and the space G/B = K/M is called the maximal or Furstenberg boundary of U2. In general, a boundary of 52 will be a space of the form G/P where P is some parabolic subgroup of G which we may assume contains B. Fixing a parabolic subgroup P of G there is a Poisson kernel
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