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Galois theory of fuchsian q-difference equations

Jacques Sauloy
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Abstract

We propose an analytical approach to the Galois theory of singular regular linear q-difference systems. We use Tannaka duality along with Birkhoff's classification scheme with the connection matrix to define and describe their Galois groups. Then we describe \emph{fundamental subgroups} that give rise to a Riemann-Hilbert correspondence and to a density theorem of Schlesinger's type.

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Jacques Sauloy. 2002-10-15. Galois theory of fuchsian q-difference equations. https://arxiv.org/abs/math/0210221

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