Cantini, Luigi and De Gier, Jan and Wheeler, Michael - Matrix product and sum rule for Macdonald polynomials

dmtcs:6419 - Discrete Mathematics & Theoretical Computer Science, April 22, 2020, DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016)
Matrix product and sum rule for Macdonald polynomials

Authors: Cantini, Luigi and De Gier, Jan and Wheeler, Michael

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.


Volume: DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016)
Published on: April 22, 2020
Submitted on: July 4, 2016
Keywords: [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]


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