  The spectral decomposition of the path space of the vertex model associated
to the vector representation of the quantized affine algebra $U_q(\hat{sl}_n)$
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 $sl_n$-module
contents of the Yangian $Y(sl_n)$-module structures of the level 1 integrable
modules of the affine Lie algebra $\hat{sl}_n$. An analogous result is obtained
also for a vertex model associated to the quantized twisted affine algebra
$U_q(A^{(2)}_{2n})$, where $Y(B_n)$ characters appear for the degeneracy of the
spectrum. The relation to the spectrum of the Haldane-Shastry and the
Polychronakos models are also discussed.
