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arXiv · 2108.00499

Eigenfunctions of a discrete elliptic integrable particle model with hyperoctahedral symmetry

Jan Felipe van Diejen·Tamás Görbe
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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.

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Jan Felipe van Diejen, Tamás Görbe. 2021-08-01. Eigenfunctions of a discrete elliptic integrable particle model with hyperoctahedral symmetry. https://doi.org/10.1007/s00220-022-04350-9

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