English

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

R2 v1 2026-06-21T11:42:53.490Z