On universal quadratic identities for minors of quantum matrices

We give a complete combinatorial characterization of homogeneous quadratic relations of “universal character” valid for minors of quantum matrices (more precisely, for minors in the quantized coordinate ring Oq(Mm,n(K)) of m×n matrices over a field K, where q∈K⁎). This is obtained as a consequence of a study of quantized minors of matrices generated by paths in certain planar graphs, called SE-graphs, generalizing the ones associated with Cauchon diagrams. Our efficient method of verifying universal quadratic identities for minors of quantum matrices is illustrated with many appealing examples.