# Special polynomials related to the supersymmetric eight-vertex model. III. Painlevé VI equation

@article{Rosengren2014SpecialPR, title={Special polynomials related to the supersymmetric eight-vertex model. III. Painlev{\'e} VI equation}, author={H. Rosengren}, journal={arXiv: Mathematical Physics}, year={2014} }

We prove that certain polynomials previously introduced by the author can be identified with tau functions of Painleve VI, obtained from one of Picard's algebraic solutions by acting with a four-dimensional lattice of Backlund transformations. For particular lines in the lattice, this proves conjectures of Bazhanov and Mangazeev. As applications, we describe the behaviour of the corresponding solutions near the singular points of Painleve VI, and obtain several new properties of our polynomials… Expand

#### 6 Citations

Special Polynomials Related to the Supersymmetric Eight-Vertex Model: A Summary

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We introduce and study symmetric polynomials, which as very special cases include polynomials related to the supersymmetric eight-vertex model, and other elliptic lattice models with $${\Delta=\pm… Expand

Sum rules for the supersymmetric eight-vertex model

- Mathematics, Physics
- 2020

The eight-vertex model on the square lattice with vertex weights a, b, c, d obeying the relation (a 2 + ab)(b 2 + ab) = (c 2 + ab)(d 2 + ab) is considered. Its transfer matrix with L = 2n + 1, n ⩾ 0,… Expand

On the transfer matrix of the supersymmetric eight-vertex model. I. Periodic boundary conditions

- Physics, Mathematics
- 2017

The square-lattice eight-vertex model with vertex weights $a,b,c,d$ obeying the relation $(a^2+ab)(b^2+ab) = (c^2+ab)(d^2+ab)$ and periodic boundary conditions is considered. It is shown that the… Expand

Series Solutions of the Non-Stationary Heun Equation

- Physics, Mathematics
- 2018

We consider the non-stationary Heun equation, also known as quantum PainleveVI, which has appeared in dierent works on quantum integrable models and conformaleld theory. We use a generalized kernel… Expand

On the elliptic $\mathfrak{gl}_2$ solid-on-solid model: functional relations and determinants

- Physics, Mathematics
- 2016

In this work we study an elliptic solid-on-solid model with domain-wall boundaries having the elliptic quantum group $\mathcal{E}_{p, \gamma}[\widehat{\mathfrak{gl}_2}]$ as its underlying symmetry… Expand

A Combinatorial Description of Certain Polynomials Related to the XYZ Spin Chain

- Physics, Mathematics
- 2020

We study the connection between the three-color model and the polynomials $q_n(z)$ of Bazhanov and Mangazeev, which appear in the eigenvectors of the Hamiltonian of the XYZ spin chain. By… Expand

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