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Galois theory of Fuchsian \(q\)-difference equations. (English) Zbl 1053.39033
Author’s summary: 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 fundamental subgroups that give rise to a Riemann-Hilbert correspondence and to a density theorem of Schlesinger’s type.

MSC:
12H10 Difference algebra
39A13 Difference equations, scaling (\(q\)-differences)
32G34 Moduli and deformations for ordinary differential equations (e.g., Knizhnik-Zamolodchikov equation)
39A05 General theory of difference equations
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