Classification of Fuchsian systems and their connection problem

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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

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Classical Analysis and ODEs, 34M35

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http://salesiana.dossiersoluciones.com/handle/123456789/214444

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0811.2916
 http://arxiv.org/abs/0811.2916

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arXiv