Classification of Fuchsian systems and their connection problem

Abstract

We review the Deligne-Simpson problem, a combinatorial structure of middle convolutions and their relation to a Kac-Moody root system discoverd by Crawley-Boevey. We show with examples that middle convolutions transform the Fuchsian systems with a fixed number of accessory parameters into fundamental systems whose spectral type is in a finite set and we give an explicit connection formula for solutions of Fuchsian differential equations without moduli.

23pages, added appendix and examples

References in corpus (1)

• Katz's middle convolution and Yokoyama's extending operation

Cited by in corpus (9)

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• Higher order Painleve system of type D^{(1)}_{2n+2} and monodromy preserving deformation
• Moduli spaces of meromorphic connections, quiver varieties, and integrable deformations
• Moduli of regular singular parabolic connections of spectral type on smooth projective curves