The q-analogue of the wild fundamental group (I)

2006/11/17 by Jean-Pierre Ramis, J. -P. Ramis, Ramis, J. -P. +3 · 1 citation
Mathematics · #FOS: Mathematics #Graph theory and applications #Quantum Algebra (math.QA) #math.QA

paper · pdf · doi:10.48550/arxiv.math/0611521

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arxiv created 2006/11/17 · openalex publication_date 2006/11/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe an explicit construction of galoisian Stokes operators for irregular linear q-difference equations. These operators are parameterized by the points of an elliptic curve minus a finite set of singularities. Taking residues at these singularities, one gets q-analogues of alien derivations which freely generate the Lie algebra of the Stokes subgroup of the Galois group.

Cited by

• On the computation of the difference Galois groups of order three equations

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• The q-analogue of the wild fundamental group and the inverse problem of the Galois theory of q-difference equations
• The q-analogue of the wild fundamental group (II)
• Algebraic construction of the Stokes sheaf for irregular linear q-difference equations
• Galois theory of fuchsian q-difference equations
• Analytic q-difference equations