Boundary measures for symmetric domains and integral formulas for the discrete Wallach points

Let B be an irreducible hermitian symmetric domain of rank tau in C-d and let G := Aut(B) the group of all biholomorphic automorphisms of B. We construct explicit integral formulas for the G-invariant inner products on spaces of holomorphic functions on B associated with the discrete Wallach points and the so-called embedded Wallach points, by means of integration on G-orbits on the boundary partial derivativeB of B and of invariant differential operators acting on symmetric domains of lower rank.