Fuchsian differential equations of order 3,...,6 with three singular points and an accessory parameter II, Equations of order 3

Abstract

Fuchsian differential equations of order 3 with three singular points and with an accessory parameter are studied. When local exponents are generic, no shift operator is found, for codimension-1 subfamilies, neither. We found shift operators for several codimension-2 subfamilies of which accessory parameter is assigned as a cubic polynomial in the local exponents. The Dotsenko-Fateev equation is one of them.