Conference Papers Discrete Mathematics and Theoretical Computer Science Year : 2020

Matrix product and sum rule for Macdonald polynomials

Abstract

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.

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hal-02173390 , version 1 (04-07-2019)

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Luigi Cantini, Jan de Gier, Michael Wheeler. Matrix product and sum rule for Macdonald polynomials. 28-th International Conference on Formal Power Series and Algebraic Combinatorics, Simon Fraser University, Jul 2016, Vancouver, Canada. ⟨10.46298/dmtcs.6419⟩. ⟨hal-02173390⟩
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