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We establish a weight-preserving bijection between the index sets of thespectral data of row-to-row and corner transfer matrices for$U_q\widehat{sl(n)}$ restricted interaction round a face (IRF) models. Theevaluation of momenta by adding Takahashi integers in the spin chain languageis shown to directly correspond to the computation of the energy of a path onthe weight lattice in the two-dimensional model. As a consequence we derivefermionic forms of polynomial analogues of branching functions for the cosets${(A^{(1)}_{n-1})_{\ell -1}\otimes (A^{(1)}_{n-1})_{1}} \over(A^{(1)}_{n-1})_{\ell}$, and establish a bosonic-fermionic polynomial identity.Comment: 36 pages, in LaTeX, uses epic.sty, eepic.sty macros (hopefully this  time the complete paper will go through!

On the Combinatorics of Row and Corner Transfer Matrices of the $A^{(1)}_{n-1}$ Restricted Face Models