Classification of Fuchsian systems and their connection problem

Details Classification of Fuchsian systems and their connection problem Classification of Fuchsian systems and their connection problem

2008-11-18

arxiv.org/abs/0811.2916v2

Mathematics

Classical Analysis and ODEs

23pages, added appendix and examples

Scientific paper

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.

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