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. International Journal of Modern Physics A, 12, 3551-3586.

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
(A⁽¹⁾_n-1) _ℓ-1 ⊗ (A⁽¹⁾_n-1)₁  over (A⁽¹⁾_n-1)_ℓ,   and establish a bosonic-fermionic polynomial identity.

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