  Berenstein, Fomin and Zelevinsky defined functions on double Bruhat cells
which they called generalized minors. By relating certain double Bruhat cells
to configuration spaces of flags, we give formulas for these generalized minors
as tensor invariants. This allows us to verify certain weight identities. The
weights of the tensor invariants can then be used to construct the quiver for
the cluster structure on the configuration space of three flags. We also show a
converse statement--that the weights of tensor invariants can by computed from
the structure of the quiver. The weight identities are important because they
are necessary for the existence of cluster structures on the moduli space of
framed local systems.
