  Let B_{(l)} be the perfect crystal for the l-symmetric tensor representation
of the quantum affine algebra U'_q(\hat{sl(n)}). For a partition mu =
(mu_1,...,mu_m), elements of the tensor product B_{(mu_1)} \otimes ... \otimes
B_{(mu_m)} can be regarded as inhomogeneous paths. We establish a bijection
between a certain large mu limit of this crystal and the crystal of an
(generally reducible) integrable U_q(\hat{sl(n)})-module, which forms a large
family depending on the inhomogeneity of mu kept in the limit. For the
associated one dimensional sums, relations with the Kostka-Foulkes polynomials
are clarified, and new fermionic formulae are presented. By combining their
limits with the bijection, we prove or conjecture several formulae for the
string functions, branching functions, coset branching functions and spinon
character formula of both vertex and RSOS types.
