Galois groups and connection matrices for \(q\)-difference equations. (English) Zbl 0844.12004

Etingof, Pavel

Electron. Res. Announc. Am. Math. Soc. 1, No. 1, 1-9 (1995).

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.

MSC:

12H10	Difference algebra
39A10	Additive difference equations

Keywords:

Galois group; matrix \(q\)-difference equation; rational coefficients; Picard-Vessiot theory; Birkhoff connection matrix

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