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

Quiver semi-invariants and SAGBI bases