Galois theory of fuchsian q-difference equations
نویسنده
چکیده
We propose an analytical approach to the Galois theory of singular regular linear q-difference systems. We use Tannaka duality along with Birkhoff’s classification scheme with the connection matrix to define and describe their Galois groups. Then we describe fundamental subgroups that give rise to a Riemann-Hilbert correspondence and to a density theorem of Schlesinger’s type.
منابع مشابه
Lectures on differential
Differential Galois theory has known an outburst of activity in the last decade. To pinpoint what triggered this renewal is probably a matter of personal taste; all the same, let me start the present review by a tentative list, restricted on purpose to “non-obviously differential” occurrences of the theory (and also, as in the book under review, to the Galois theory of linear differential equat...
متن کاملOn globally nilpotent differential equations
In a previous work of the authors, a middle convolution operation on the category of Fuchsian differential systems was introduced. In this note we show that the middle convolution of Fuchsian systems preserves the property of global nilpotence. This leads to a globally nilpotent Fuchsian system of rank two which does not belong to the known classes of globally nilpotent rank two systems. Moreov...
متن کاملGalois groups of the basic hypergeometric equations 1 by Julien Roques 20 th of August 2007
In this paper we compute the Galois groups of basic hypergeometric equations. In this paper q is a complex number such that 0 < |q| < 1. 1 Basic hypergeometric series and equations The theory of hypergeometric functions and equations dates back at least as far as Gauss. It has long been and is still an integral part of the mathematical literature. In particular, the Galois theory of (generalize...
متن کاملGalois groups of the basic hypergeometric equations 1 by
In this paper we compute the Galois groups of basic hypergeometric equations. In this paper q is a complex number such that 0 < |q| < 1. 1 Basic hypergeometric series and equations The theory of hypergeometric functions and equations dates back at least as far as Gauss. It has long been and is still an integral part of the mathematical literature. In particular, the Galois theory of (generalize...
متن کاملOn classical irregular q-difference equations
The primary aim of this paper is to (provide tools in order to) compute Galois groups of classical irregular q-difference equations. We are particularly interested in quantizations of omnipresent differential equations in the mathematical and physical literature, namely confluent generalized q-hypergeometric equations and q-Kloosterman equations.
متن کامل