On the combinatorics of row and corner transfer matrices of the $A_{n-1}^{(1)}$ 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 $U_q\widehat{sl(n)}$ 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 $\frac{(A_{n-1}^{(1)}{)}_{\ell -1}\otimes (A_{n-1}^{(1)}{)}_1}{(A_{n-1}^{(1)}{)}_{\ell }}$, and establish a bosonic-fermionic polynomial identity.

36 pages, in LaTeX, uses epic.sty, eepic.sty macros (hopefully this time the complete paper will go through!)

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