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

Abstract

We establish a weight-preserving bijection between the index sets of the spectral data of row-to-row and corner transfer matrices for [Formula: see text] 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 analogs of branching functions for the cosets [Formula: see text], and establish a bosonic–fermionic polynomial identity.