Invariant fundamental solutions for invariant differential operators on reductive symmetric spaces of type GC/GR

Let G be a complex connected reductive group with simply connected derived group. Let H be a real form of G. Let z be a G-invariant differential operator on the reductive symmetric space G/H. We give an explicit sufficient condition for z to have an invariant fundamental solution on G/H. (C) Academie des Sciences/Elsevier, Paris.