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arXiv · 2110.13860

q-Heun equation and initial-value space of q-Painlev\'e equation

Shoko Sasaki·Shun Takagi·Kouichi Takemura
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Abstract

We show that the q-Heun equation and its variants appear in the linear q-difference equations associated to some q-Painlev\'e equations by considering the blow-up associated to their initial-value spaces. We obtain the firstly degenerated Ruijsenaars-van Diejen operator from the linear q-difference equation associated to the q-Painlev\'e equation of type $E_8$.

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Shoko Sasaki, Shun Takagi, Kouichi Takemura. 2021-10-26. q-Heun equation and initial-value space of q-Painlev\'e equation. https://arxiv.org/abs/2110.13860

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