Skew Young diagram method in spectral decomposition of integrable lattice models

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The spectral decomposition of the path space of the vertex model associated to the vector representation of the quantized affine algebra Uq(slₙ) is studied. We give a one-to-one correspondence between the spin configurations and the semi-standard tableaux of skew Young diagrams. As a result we obtain a formula of the characters for the degeneracy of the spectrum in terms of skew Schur functions. We conjecture that our result describes the slₙ-module contents of the Yangian Y(slₙ)-module structures of the level 1 integrable modules of the affine Lie algebra slₙ. An analogous result is obtained also for a vertex model associated to the quantized twisted affine algebra Uq(A⁽²⁾₂ₙ), where Y(Bₙ) characters appear for the degeneracy of the spectrum. The relation to the spectrum of the Haldane-Shastry and the Polychronakos models are also discussed.