  It is known that there exist Calabi-Yau structures on the complexifications
of symmetric spaces of compact type. In this paper, we describe the Calabi-Yau
structures of the complexified symmetric spaces in terms of the Schwarz's
theorem in detail. We consider the case where the Calabi-Yau structure arises
from the Riemannian metric corresponding to the Stenzel metric. In the
complexified symmetric spaces equipped with such a Calabi-Yau structure, we
give constructions of special Lagrangian submanifolds of any phase which are
invariant under the actions of symmetric subgroups of the isometry group of the
original symmetric space of compact type.
