The eight-vertex model on the square lattice with vertex weights a, b, c, d obeying the relation (a² + ab)(b² + ab) = (c² + ab)(d² + ab) is considered. Its transfer matrix with L = 2n + 1, n ⩾ 0, vertical lines and periodic boundary conditions along the horizontal direction has the doubly-degenerate eigenvalue Θ_n = (a + b)²ⁿ⁺¹. A basis of the corresponding eigenspace is investigated. Several scalar products involving the basis vectors are computed in terms of a family of polynomials introduced by Rosengren and Zinn-Justin. These scalar products are used to find explicit expressions for particular entries of the vectors. The proofs of these results are based on the generalisation of the eigenvalue problem for Θ_n to the inhomogeneous eight-vertex model.

考虑满足（a ² + ab）（b ² + ab）=（c ² + ab）（d ² + ab）的关系，具有权重a，b，c和d的方格上的八顶点模型。它与传递矩阵大号= 2 Ñ + 1，Ñ ⩾0，垂直线和周期性边界条件沿水平方向具有双简并本征值Θ _Ñ =（一个+ b）^{2 n +1}。研究了相应特征空间的基础。根据Rosengren和Zinn-Justin引入的多项式族来计算涉及基向量的几个标量积。这些标量积用于查找向量的特定条目的显式表达式。这些结果的证明是基于特征值问题的概括为Θ _ñ的不均匀八顶点模型。