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Galois Groups and Connection Matrices for q-Difference Equations
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## Galois groups and connection matrices for q-difference equations

### Pavel I. Etingof

**Abstract.**
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 `

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