Geodesic
Matrix product and sum rule for Macdonald polynomials
Discrete mathematics & theoretical computer science, DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016), DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016) (2020).

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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. 
@article{DMTCS_2020_special_379_a101,
     author = {Cantini, Luigi and De Gier, Jan and Wheeler, Michael},
     title = {Matrix product and sum rule for {Macdonald} polynomials},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016)},
     year = {2020},
     doi = {10.46298/dmtcs.6419},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.6419/}
}
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%A De Gier, Jan
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%T Matrix product and sum rule for Macdonald polynomials
%J Discrete mathematics & theoretical computer science
%D 2020
%V DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016)
%I mathdoc
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Cantini, Luigi; De Gier, Jan; Wheeler, Michael. Matrix product and sum rule for Macdonald polynomials. Discrete mathematics & theoretical computer science, DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016), DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016) (2020). doi : 10.46298/dmtcs.6419. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.6419/

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