arXiv subjects

Shoko Sasaki

Publications and source records attributed to Shoko Sasaki.

2 recordsLinked to original sources

arXiv2022

$q$-Middle Convolution and $q$-Painlevé Equation

A $q$-deformation of the middle convolution was introduced by Sakai and Yamaguchi. We apply it to a linear $q$-difference equation associated with the $q$-Painlevé VI equation. Then we obtain integral transformations. We investigate the $q$-middle convolution in terms of the affine Weyl group symmetry of the $q$-Painlevé VI equation. We deduce an integral transformation on the $q$-Heun equation.

math.CA↗

arXiv2021

q-Heun equation and initial-value space of q-Painlevé equation

We show that the q-Heun equation and its variants appear in the linear q-difference equations associated to some q-Painlevé 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-Painlevé equation of type $E_8$.

math.CA↗