arXiv math/04033782004-03math.GMmath.CAmath.GR

On the Constructive Inverse Problem in Differential Galois Theory

William J. Cook, Claude Mitschi, Michael F. Singer

备注：: Several misprints have been corrected and the statement of Propositions 3.2 and 3.4 have been made more precise and their proofs expanded

英文摘要：

We give sufficient conditions for a linear differential equation to have a given semisimple group as its Galois group. For any linear algebraic group G given as a semidirect product of a finite subgroup and a normal subgroup that is a product of groups of type An, Cn, Dn, E6, or E7, we construct a differential equation over C(x) having Galois group G.

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