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ISSN 1079-6762

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
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

DOI: http://dx.doi.org/10.1090/S1079-6762-95-01001-8
PII: S 1079-6762(95)01001-8
Received by editor(s): April 6, 1995
Communicated by: David Kazhdan
Article copyright: © Copyright 1995 American Mathematical Society