On the combinatorics of row and corner transfer matrices of the $A_{n-1}^{(1)}$ restricted face models

Details On the combinatorics of row and corner transfer matrices of the $A_{n-1}^{(1)}$ restricted face models On the combinatorics of row and corner transfer matrices of the $A_{n-1}^{(1)}$ restricted face models

1995-12-13

arxiv.org/abs/hep-th/9512095v2

Int.J.Mod.Phys. A12 (1997) 3551-3586

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1142/S0217751X97001845

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.

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