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

TL;DR

This paper demonstrates that the partition function of the higher spin 6-vertex model with domain wall boundary conditions simplifies to a Macdonald polynomial at a specific crossing parameter, extending known results from Schur polynomials.

Contribution

It establishes a connection between the higher spin 6-vertex model's partition function and Macdonald polynomials at the combinatorial point, generalizing previous results involving Schur polynomials.

Findings

Partition function reduces to Macdonald polynomial at the combinatorial point.

Extends known results from Schur to Macdonald polynomials.

Provides a new algebraic structure for higher spin models.

Abstract

The determinantal form of the partition function of the 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-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.