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arXiv · 2606.06863

Rational Heun operators on $q$-linear grids

Satoshi Tsujimoto·Luc Vinet·Alexei Zhedanov
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Abstract

Rational Heun operators on the $q-$linear grid are presented. They are second-order $q-$difference operators $W_q$ constructively defined from the requirement that they have a raising action on rational functions of type $[n/n]$, namely $W_q: [n/n] \rightarrow [n+1/n+1]$, with poles on $q-$linear grids. It will be observed that these operators are related to one family of the Ruijsenaars-van Diejen-Takemura Hamiltonians. A distinguished subclass of $W_q$ called classical which shifts the pole structure while preserving the rational function type and a prescribed basis is also characterized.

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Satoshi Tsujimoto, Luc Vinet, Alexei Zhedanov. 2026-06-05. Rational Heun operators on $q$-linear grids. https://arxiv.org/abs/2606.06863

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