  Starting from the geometrical construction of special Lagrangian submanifolds
of a toric variety, we identify a certain subclass of A-type D-branes in the
linear sigma model for a Calabi-Yau manifold and its mirror with the A- and
B-type Recknagel-Schomerus boundary states of the Gepner model, by reproducing
topological properties such as their labeling, intersection, and the
relationships that exist in the homology lattice of the D-branes. In the
non-linear sigma model phase these special Lagrangians reproduce an old
construction of 3-cycles relevant for computing periods of the Calabi-Yau, and
provide insight into other results in the literature on special Lagrangian
submanifolds on compact Calabi-Yau manifolds. The geometrical construction of
rational boundary states suggests several ways in which new Gepner model
boundary states may be constructed.
