Eigenfunctions of a Discrete Elliptic Integrable Particle Model with Hyperoctahedral Symmetry

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