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Abstract

We present a worked example for the new extensions of the multi-particle Calogero model endowed with infiniteWeyl group symmetry of affine and hyperbolic type. Building upon the hyperbolic extension of the A3-Kac-Moody algebra, we construct an explicit realisation of the model in terms of infinite root systems generated from Coxeter orbits. To address the challenge of summing over infinitely many roots, we introduce root string representatives that span the invariant root space while preserving invariance under the affine Weyl group. This approach yields closed-form expressions for the potentials, which by construction are invariant under the full affine Weyl symmetry. Moreover, we demonstrate that in an appropriate infinite-coordinate limit the model reduces smoothly to the conventional four particle A3-Calogero system. Our construction constitutes a systematic method for implementing infinite-dimensional symmetries into Calogero-type models, thus broadening their algebraic and physical applicability.

Publication Type:	Article
Additional Information:	Content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
Subjects:	Q Science > QC Physics
Departments:	School of Science & Technology School of Science & Technology > Department of Mathematics
SWORD Depositor:	Symplectic Administrator

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