Abstract
A special class of integrable Fuchsian systems on C n related to KZ equations is considered. We survey the construction of such systems and the list of the structural properties their monodromy representations. The relation of the Fuchsian systems obtained by the Veselov construction assosiated with a deformation of the A n−1-type root system and the Gauss–Manin connection of the natural projection C n→C n−1 is described. In this case, we prove that the monodromy representation is equivalent to the Burau representation of the Artin braid group. For a deformations of the other root system, we introduce generalized Burau representations. We conjecture that the integrable Fuchsian systems related to essential new finite sets of the vectors described by Veselov and Chalykh are the result of the Klares–Schlesinger isomonodromic deformations (or transformation) of the integrable Fuchsian system related to the Coxeter root systems.
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Lexin, V.P. Monodromy of Rational KZ Equations and Some Related Topics. Acta Applicandae Mathematicae 75, 105–115 (2003). https://doi.org/10.1023/A:1022327709909
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DOI: https://doi.org/10.1023/A:1022327709909