Strings, paths, and standard tableaux

Abstract

For the vacuum sectors of regime-III ABF models, we observe that two sets of combinatorial objects: the strings which parametrize the row-to-row transfer matrix eigenvectors, and the paths which parametrize the corner transfer matrix eigenvectors, can both be expressed in terms of the same set of standard tableaux. Furthermore, the momenta of the strings, the energies of the paths, and the charges of the tableaux are such that there is a weight-preserving bijection between the two sets of eigenvectors, wherein the tableaux play an interpolating role. This bijection is so natural, that we conjecture that it exists in general.