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Galois groups and connection matrices for \(q\)-difference equations. (English) Zbl 0844.12004
Summary: We study the Galois group of a matrix \(q\)-difference equation with rational coefficients which is regular at \(0\) and \(\infty\), in the sense of (difference) Picard-Vessiot theory, and show that it coincides with the algebraic group generated by matrices \(C(z) C(w)^{-1}\), \(z, w \in C^*\), where \(C(z)\) is the Birkhoff connection matrix of the equation.

12H10 Difference algebra
39A10 Additive difference equations
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