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Differential Equations and Finite Groups

✍ Scribed by Marius van der Put; Felix Ulmer

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
311 KB
Volume
226
Category
Article
ISSN
0021-8693

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✦ Synopsis

The classical solution of the Riemann᎐Hilbert problem attaches to a given representation of the fundamental group a regular singular linear differential equation. We present a method to compute this differential equation in the case of a representation with finite image. The approach uses Galois coverings of P 1 _ Γ„ 4 0, 1, Ο± , differential Galois theory, and a formula for the character of the Galois action of the space of holomorphic differentials. Examples are produced for the finite primitive unimodular groups of degree two and three.

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