Luigi Cantini ; Jan De Gier ; Michael Wheeler - 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) - https://doi.org/10.46298/dmtcs.6419
Matrix product and sum rule for Macdonald polynomials

Authors: Luigi Cantini 1; Jan De Gier ; Michael Wheeler ORCID-iD2

  • 1 Laboratoire de Physique Théorique et Modélisation
  • 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.

https://doi.org/10.46298/dmtcs.6419
Source: HAL:hal-02173390v1
Volume: DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016)
Published on: April 22, 2020
Imported on: July 4, 2016
Keywords: [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]

Linked publications - datasets - softwares

Source : ScholeXplorer IsRelatedTo ARXIV 1205.1471
Source : ScholeXplorer IsRelatedTo DOI 10.1016/j.nuclphysb.2014.06.017
Source : ScholeXplorer IsRelatedTo DOI 10.48550/arxiv.1205.1471
  • 1205.1471
  • 10.1016/j.nuclphysb.2014.06.017
  • 10.48550/arxiv.1205.1471
Asymptotic representations and q-oscillator solutions of the graded Yang–Baxter equation related to Baxter Q-operators

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