A Classification of Roots of Symmetric Kac-Moody Root Systems and Its Application

Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 40)


We study Weyl group orbits in symmetric Kac-Moody root systems and show a finiteness of orbits of roots with a fixed index. We apply this result to the study of the Euler transform of linear ordinary differential equations on the Riemann sphere whose singular points are regular singular or unramified irregular singular points. The Euler transform induces a transformation on spectral types of the differential equations and it keeps their indices of rigidity. Then as a generalization of the result by Oshima (in Fractional calculus of Weyl algebra and Fuchsian differential equations, MSJ Memoirs 28, 2012), we show a finiteness of Euler transform orbits of spectral types with a fixed index of rigidity.


Singular Point Weyl Group Spectral Type Dynkin Diagram Fixed Index 
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© Springer-Verlag London 2013

Authors and Affiliations

  1. 1.Research Institute for Mathematical SciencesKyoto UniversityKyotoJapan
  2. 2.Graduate School of Mathematical SciencesThe University of TokyoMeguro-ku, TokyoJapan

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