Eigenfunctions of a discrete elliptic integrable particle model with hyperoctahedral symmetry

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.

23 pages

References in corpus (4)

• Hilbert-Schmidt Operators vs. Integrable Systems of Elliptic Calogero-Moser Type IV. The Relativistic Heun (van Diejen) Case
• Complex hypergeometric functions and integrable many-body problems
• Elliptic Ruijsenaars difference operators on bounded partitions
• Elliptic Racah polynomials