Classification of Fuchsian systems and their connection problem
Classical Analysis and ODEs
2009-01-07 v2
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.
Keywords
Cite
@article{arxiv.0811.2916,
title = {Classification of Fuchsian systems and their connection problem},
author = {Toshio Oshima},
journal= {arXiv preprint arXiv:0811.2916},
year = {2009}
}
Comments
23pages, added appendix and examples