The higher spin generalization of the 6-vertex model with domain wall boundary conditions and Macdonald polynomials

Abstract

The determinantal form of the partition function of the $$6$$6-vertex model with domain wall boundary conditions was given by Izergin. It is known that for a special value of the crossing parameter the partition function reduces to a Schur polynomial. Caradoc, Foda and Kitanine computed the partition function of the higher spin generalization of the $$6$$6-vertex model. In the present work, it is shown that for a special value of the crossing parameter, referred to as the combinatorial point, the partition function reduces to a Macdonald polynomial.