Authors: Luigi Cantini ¹; Jan De Gier ; Michael Wheeler ²

• 1 Laboratoire de Physique Théorique et Modélisation [LPTM - UMR 8089]
• 2 Department of Mathematics and Statistics [Melbourne]

We present a new, explicit sum formula for symmetric Macdonald polynomials Pλ and show that they can be written as a trace over a product of (infinite dimensional) matrices. These matrices satisfy the Zamolodchikov– Faddeev (ZF) algebra. We construct solutions of the ZF algebra from a rank-reduced version of the Yang–Baxter algebra. As a corollary, we find that the normalization of the stationary measure of the multi-species asymmetric exclusion process is a Macdonald polynomial with all variables set equal to one.