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
U
q
sl(n)
ˆ
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
(
A
(1)
n−1
)
ℓ
, and establish a bosonic-fermionic polynomial identity.