Affine Weyl groups and non-Abelian discrete systems: an application to the d-Painlevé equations

2024/03/27 by Bobrova, Irina · 2 citations
#Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences

paper · doi:10.48550/arxiv.2403.18463

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 ≥ 2 type and of d-Painlevé equations with an additive dynamic were derived. A coalescence cascade of the later is also discussed.

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• On a non-commutative sixth q-Painlevé system: from discrete system to surface theory
• A non-commutative discrete first Painlevé hierarchy: the Lax pair approach

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