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

Abstract

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 $E_8$.

24 pages

References in corpus (1)

• Middle Convolution and Heun's Equation

Cited by in corpus (1)

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