Degenerations of Ruijsenaars-van Diejen operator and q-Painleve equations

Abstract: It is known that the Painleve VI is obtained by connection preserving deformation of some linear differential equations, and the Heun equation is obtained by a specialization of the linear differential equations. We inverstigate degenerations of the Ruijsenaars-van Diejen difference opearators and show difference analogues of the Painleve-Heun correspondence.