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arXiv · 2403.18463

Affine Weyl groups and non-Abelian discrete systems: an application to the $d$-Painlev\'e equations

Irina Bobrova
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Abstract

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 $d$-Painlev\'e equations with an additive dynamic were derived. A coalescence cascade of the later is also discussed.

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Irina Bobrova. 2024-03-27. Affine Weyl groups and non-Abelian discrete systems: an application to the $d$-Painlev\'e equations. https://doi.org/10.1007/s11040-026-09573-z

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