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Affine Weyl groups and non-Abelian discrete systems: an application to the $d$-Painlevé equations
A non-abelian generalisation of a birational representation of affine Weyl groups and their application to the discrete dynamical systems is presented. By using this generalisation, non-commutative analogs for the discrete systems of $A_n^{(1)}$, $n \geq 2$ type and of $d$-Painlevé equations with an
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