Skew Young diagram method in spectral decomposition of integrable lattice models II: Higher levels Original Research Article

The spectral decomposition of the path space_ of the vertex model associated to the level-l representation of the quantized affine algebra Uq(ŝln) is studied. The spectrum and its degeneracy are parametrized by skew Young diagrams and what we call non-movable tableaux on them, respectively. As a result we obtain the characters for the degeneracy of the spectrum in terms of an alternating sum of skew Schur functions. Also studied are new combinatorial descriptions (spectral decomposition) of the Kostka numbers and the Kostka-Foulkes polynomials. As an application we give a new proof of Nakayashiki-Yamadaʹs theorem about the branching functions of the level-l basic representation l GGk of ŝln and a generalization of the theorem.