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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.

Copyright American Mathematical Society 1995

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Article Info

• ERA Amer. Math. Soc. 01 (1995), pp. 1-9
• Publisher Identifier: S 1079-6762(95)01001-8
• 1991 Mathematics Subject Classification. 12H10; 39A10 .
• Received by the editors April 6, 1995
• Communicated by David Kazhdan
• Comments (When Available)

Pavel I. Etingof

Department of Mathematics, Harvard University, Cambridge, MA 02138, USA.

E-mail address: etingof@math.harvard.edu