Title: A combinatorial description of certain polynomials related to the XYZ spin chain
Abstract: Bazhanov and Mangazeev studied certain polynomials q_n(z) which appear in the eigenvectors of the Hamiltonian of the XYZ spin chain. These polynomials seem to have positive integer coefficients, which suggests that there should be a combinatorial interpretation. By studying the bijection between the alternating sign matrices and the states of the six-vertex model with domain wall boundary conditions (DWBC), Kuperberg proved the alternating sign matrix conjecture of Mills, Robins and Rumsey. In this talk, we specialize the parameters in the partition function of the eight-vertex solid-on-solid model with DWBC and one reflecting end in Kuperberg's way, which yields an explicit combinatorial expression for q_n(z) in terms of the partition function of the three-color model with the same boundary conditions.
Alexi Morin-Duchesne
