  Functional equations, in the form of fusion hierarchies, are studied for the
transfer matrices of the fused restricted $A_{n-1}^{(1)}$ lattice models of
Jimbo, Miwa and Okado. Specifically, these equations are solved analytically
for the finite-size scaling spectra, central charges and some conformal
weights. The results are obtained in terms of Rogers dilogarithm and correspond
to coset conformal field theories based on the affine Lie algebra
$A_{n-1}^{(1)}$ with GKO pair $A^{(1)}_{n-1}\; \oplus A^{(1)}_{n-1}\;\supset \;
A^{(1)}_{n-1}$.
