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

@article{Rosengren2015SpecialPR, title={Special Polynomials Related to the Supersymmetric Eight-Vertex Model: A Summary}, author={Hjalmar Rosengren}, journal={Communications in Mathematical Physics}, year={2015}, volume={340}, pages={1143-1170} }

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 $${\Delta=\pm 1/2}$$Δ=±1/2. There is also a close relation to affine Lie algebra characters. After a natural change of variables, our polynomials satisfy a non-stationary Schrödinger equation with elliptic potential, which is related to the Knizhnik–Zamolodchikov–Bernard equation and to the canonical quantization…

## 19 Citations

### Sum rules for the supersymmetric eight-vertex model

- MathematicsJournal of Statistical Mechanics: Theory and Experiment
- 2021

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,…

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

- Mathematics, Physics
- 2017

The square-lattice eight-vertex model with vertex weights a,b,c,d obeying the relation (a2+ab)(b2+ab)=(c2+ab)(d2+ab) and periodic boundary conditions is considered. It is shown that the transfer…

### Elliptic pfaffians and solvable lattice models

- Mathematics
- 2016

We introduce and study twelve multivariable theta functions defined by pfaffians with elliptic function entries. We show that, when the crossing parameter is a cubic root of unity, the domain wall…

### On the transfer matrix of the supersymmetric eight-vertex model. II. Open boundary conditions

- PhysicsJournal of Statistical Mechanics: Theory and Experiment
- 2020

The transfer matrix of the square-lattice eight-vertex model on a strip with vertical lines and open boundary conditions is investigated. It is shown that for vertex weights that obey the relation…

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

- MathematicsSymmetry, Integrability and Geometry: Methods and Applications
- 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…

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

- 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…

### On the elliptic 𝔤𝔩2 solid-on-solid model: Functional relations and determinants

- MathematicsJournal of Mathematical Physics
- 2019

In this work, we study an elliptic solid-on-solid model with domain-wall boundaries having the elliptic quantum group Ep,γ[gl2^] as its underlying symmetry algebra. We elaborate on results previously…

### Nearest-neighbour correlation functions for the supersymmetric XYZ spin chain and Painlev\'e VI

- Physics
- 2022

. We study nearest-neighbour correlation functions for the ground state of the supersymmetric XYZ spin chain with odd length and periodic boundary conditions. Under a technical assumption related to…

### Isomonodromic quantization of the second Painlevé equation by means of conservative Hamiltonian systems with two degrees of freedom

- MathematicsSt. Petersburg Mathematical Journal
- 2022

For the three nonstationary Schrödinger equations
i
ℏ
Ψ
τ
=
H
(
x
,
y
,
−
i
ℏ
∂
∂
x
,
−
i
ℏ
∂
∂
y
)
Ψ
,
\begin{equation*} i\hbar \Psi…

### Solutions of the analogues of time-dependent Schrödinger equations corresponding to a pair of $$H^{3+2}$$ Hamiltonian systems

- MathematicsTheoretical and Mathematical Physics
- 2022

We construct joint 2 × 2 matrix solutions of the scalar linear evolution equations Ψ (cid:2) s k = H 3+2 s k ( s 1 , s 2 , x 1 , x 2 , ∂/∂x 1 , ∂/∂x 2 )Ψ with times s 1 and s 2 , which can be treated…

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