Determination of the symmetry group for some QRT roots

2023/05/26 by Giorgio Gubbiotti, Yang Shi, Gubbiotti, Giorgio +1
Computer Science · Mathematics · #14H70 #17B22 #39A36 #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Group Theory (math.GR) #Mathematical Physics (math-ph) #Mathematics and Applications #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2305.17107

openalex publication_date 2023/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We determine the affine Weyl symmetries of some two-dimensional birational maps known as QRT roots arising from Kahan--Hirota--Kimura discretisation of two different reduced Nahm systems. The main finding is that the symmetry types of these discrete systems are subgroups of the Weyl groups for Sakai's discrete Painlevé equations to which the QRT maps are the autonomous limits.

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