Galois theory of fuchsian q-difference equations

Details Galois theory of fuchsian q-difference equations Galois theory of fuchsian q-difference equations

2002-10-15

arxiv.org/abs/math/0210221v1

Mathematics

Quantum Algebra

Prepublication du Laboratoire Emile Picard n.246. See also http://picard.ups-tlse.fr

Scientific paper

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 \emph{fundamental subgroups} that give rise to a Riemann-Hilbert correspondence and to a density theorem of Schlesinger's type.

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