Title: Eigenfunctions of a discrete elliptic integrable particle model with hyperoctahedral symmetry Show Chinese title

Title: 离散椭圆可积粒子模型的特征函数具有超八面体对称性

Abstract: We construct the orthogonal eigenbasis for a discrete elliptic Ruijsenaars type quantum particle Hamiltonian with hyperoctahedral symmetry. In the trigonometric limit the eigenfunctions in question recover a previously studied $q$-Racah type reduction of the Koornwinder-Macdonald polynomials. When the inter-particle interaction degenerates to that of impenetrable bosons, the orthogonal eigenbasis simplifies in terms of generalized Schur polynomials on the spectrum associated with recently found elliptic Racah polynomials. Show Chinese abstract

Abstract: 我们为具有超八面体对称性的离散椭圆Ruijsenaars型量子粒子哈密顿量构建了正交本征基。 在三角极限下，所讨论的本征函数恢复了之前研究过的 Koornwinder-Macdonald 多项式的$q$-Racah 型约简。 当粒子间相互作用退化为不可穿透玻色子的情况时，正交本征基在与最近发现的椭圆Racah多项式相关的谱上简化为广义Schur多项式。