NONSYMMETRIC MACDONALD POLYNOMIALS VIA INTEGRABLE VERTEX MODELS

Starting from an integrable rank-n vertex model, we construct an explicit family of partition functions indexed by compositions mu = (mu(1), ..., mu(n)). Using the Yang-Baxter algebra of the model and a certain rotation operation that acts on our partition functions, we show that they are eigenfunctions of the Cherednik-Dunkl operators Y-i for all 1 <= i <= n, and are thus equal to nonsymmetric Macdonald polynomials E-mu. Our partition functions have the combinatorial interpretation of ensembles of coloured lattice paths which traverse a cylinder. Applying a simple bijection to such path ensembles, we show how to recover the well-known combinatorial formula for E-mu due to Haglund-Haiman-Loehr.