Galois groups and connection matrices of $q$-difference equations

Author:
Pavel I. Etingof

Journal:
Electron. Res. Announc. Amer. Math. Soc. **1** (1995), 1-9

MSC (1991):
Primary 12H10, 39A10

DOI:
https://doi.org/10.1090/S1079-6762-95-01001-8

MathSciNet review:
1336694

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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 $C(u)C(w)^{-1}$ $u,w\in \mathbb {C}^*$, where $C(z)$ is the Birkhoff connection matrix of the equation.

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Additional Information

**Pavel I. Etingof**

Affiliation:
address Department of Mathematics, Harvard University, Cambridge, MA 02138, USA.

Email:
etingof@math.harvard.edu

Received by editor(s):
April 6, 1995

Communicated by:
David Kazhdan

Article copyright:
© Copyright 1995
American Mathematical Society