Algorithm classifying roots of star-shaped Kac-Moody root systems

Published 3 Apr 2025 in math.RT, math-ph, math.CA, math.MP, and nlin.SI | (2504.18542v1)

Abstract: For a star-shaped Kac-Moody root system, we provide an effective algorithm to obtain representatives of the Weyl group orbits of roots with a given norm and implement it as a computer program. We also explain the relationship between these orbits and Fuchsian differential equations on the Riemann sphere, as well as higher-dimensional Painleve-type equations.

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Toshio Oshima

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