On globally nilpotent differential equations

Details On globally nilpotent differential equations On globally nilpotent differential equations

2006-05-15

arxiv.org/abs/math/0605383v4

Mathematics

Algebraic Geometry

Scientific paper

In a previous work of the authors, a middle convolution operation on the category of Fuchsian differential systems was introduced. In this note we show that the middle convolution of Fuchsian systems preserves the property of global nilpotence. This leads to a globally nilpotent Fuchsian system of rank two which does not belong to the known classes of globally nilpotent rank two systems. Moreover, we give a globally nilpotent Fuchsian system of rank seven whose differential Galois group is isomorphic to the exceptional simple algebraic group of type $G_2.$

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