Linear differential equations with finite differential Galois group (Q2306648)

The paper is devoted to the inverse problem of Galois theory for a finite group \(G\) and the ordinary differential field \(C(z)\) with the derivation \(\delta=\frac{d}{dz}\) and \(C\) is an algebraically closed field of characteristic zero. The authors represent the algorithm for constructing a standard linear differential operator, which sets the Picard-Vessiot extension of \(C(z)\) with the Galois group \(G\). It is assumed that \(G\) is an irreducible subgroup of \(\mathrm{PSL}(C^n)\), acts on an irreducible curve \(\varGamma\subset\mathbb{P}(C^n)\), so that \(C(\varGamma)^G=C(z)\). The algorithm presented is tested for \(n=2\) and for three irreducible subgroups of \(\mathrm{SL}_3\).