  We introduce a new combinatorial structure of linked tableaux, which
generalize the semi-standard tableaux that index a SAGBI basis of the Pl\"ucker
coordinate ring of a flag variety. We show that linked tableaux index
Domokos-Zubkov semi-invariants, which generate the semi-invariant ring of a
quiver, which in many cases coincides with the Cox ring of an associated quiver
moduli space. We show that these semi-invariants satisfy straightening laws. In
the case of the generalized Kronecker quiver, we prove that the semi-invariants
associated to semi-standard linked tableaux are a (possibly infinite) SAGBI
basis. For the generalized Kronecker quiver with dimension vector (2,2), we
show that the SAGBI basis is finite and describe it explicitly.
