Middle convolution of Fuchsian systems and the construction of rigid differential systems

Titelangaben

Dettweiler, Michael ; Reiter, Stefan:
Middle convolution of Fuchsian systems and the construction of rigid differential systems.
In: Journal of Algebra. Bd. 318 (2007) Heft 1 . - S. 1-24.
ISSN 1090-266X
DOI: https://doi.org/10.1016/j.jalgebra.2007.08.029

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Abstract

In [M. Dettweiler, S. Reiter, An algorithm of Katz and its application to the inverse Galois problem, J. Symbolic Comput. 30 (2000) 761–798], a purely algebraic analogon of Katz' middle convolution functor (see [N.M. Katz, Rigid Local Systems, Ann. of Math. Stud., vol. 139, Princeton University Press, 1997]) is given. In this paper, we find an explicit Riemann–Hilbert correspondence for this functor. This leads to a construction algorithm for differential systems which correspond to rigid local systems on the punctured affine line via the Riemann–Hilbert correspondence.