Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 18 (2022), 036, 20 pages      arXiv:2104.04651      https://doi.org/10.3842/SIGMA.2022.036

A Combinatorial Description of Certain Polynomials Related to the XYZ Spin Chain. II. The Polynomials $p_n$

Linnea Hietala ab
a) Department of Mathematics, Uppsala University, Box 480, 751 06 Uppsala, Sweden
b) Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, 412 96 Gothenburg, Sweden

Received August 06, 2021, in final form April 29, 2022; Published online May 15, 2022

Abstract
By specializing the parameters in the partition function of the 8VSOS model with domain wall boundary conditions and diagonal reflecting end, we find connections between the three-color model and certain polynomials $p_n(z)$, which are conjectured to be equal to certain polynomials of Bazhanov and Mangazeev, appearing in the eigenvectors of the Hamiltonian of the supersymmetric XYZ spin chain. This article is a continuation of a previous paper where we investigated the related polynomials $q_n(z)$, also conjectured to be equal to polynomials of Bazhanov and Mangazeev, appearing in the eigenvectors of the supersymmetric XYZ spin chain.

Key words: eight-vertex SOS model; domain wall boundary conditions; reflecting end; three-color model; XYZ spin chain; polynomials; positive coefficients.

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