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For the three Fuchsian differential equations of order 4, 5 and 6, connectedwith the Dotsenko-Fateev equation of order 3, via addition and middleconvolution, we find shift operators and reducibility conditions, and studyreducible cases.

Fuchsian differential equations of order 3,...,6 with three singular  points and an accessory parameter III, Higher order versions of the  Dotsenko-Fateev equation