# On the combinatorics of row and corner transfer matrices of the $A_n-1^(1)$ restricted face models

Dasmahapatra, Srinandan (1997) On the combinatorics of row and corner transfer matrices of the $A_n-1^(1)$ restricted face models. nternational Journal of Modern Physics A 12, 12, 3551-3586.

We establish a weight-preserving bijection between the index sets of the spectral data of row-to-row and corner transfer matrices for $U_q\widehat{sl(n)}$ restricted interaction round a face (IRF) models. The evaluation of momenta by adding Takahashi integers in the spin chain language is shown to directly correspond to the computation of the energy of a path on the weight lattice in the two-dimensional model. As a consequence we derive fermionic 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.