Deformed cluster maps of type $A_{2N}$

Fuente: arXiv
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Main Authors: Grabowski, Jan E., Hone, Andrew N. W., Kim, Wookyung
Format: Preprint
Published: 2024
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author Grabowski, Jan E.
Hone, Andrew N. W.
Kim, Wookyung
author_facet Grabowski, Jan E.
Hone, Andrew N. W.
Kim, Wookyung
contents We extend recent work of the third author and Kouloukas by constructing deformations of integrable cluster maps corresponding to the Dynkin types $A_{2N}$, lifting these to higher-dimensional maps possessing the Laurent property and demonstrating integrality of the deformations for $N\leq 3$. This provides the first infinite class of examples (in arbitrarily high rank) of such maps and gives information on the associated discrete integrable systems. Key to our approach is a ``local expansion'' operation on quivers which allows us to construct and study mutations in type $A_{2N}$ from those in type $A_{2(N-1)}$.
format Preprint
id arxiv_https___arxiv_org_abs_2402_18310
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Deformed cluster maps of type $A_{2N}$
Grabowski, Jan E.
Hone, Andrew N. W.
Kim, Wookyung
Exactly Solvable and Integrable Systems
Dynamical Systems
Quantum Algebra
37J70 (Primary) 13F60, 39A36, 81R12 (Secondary)
We extend recent work of the third author and Kouloukas by constructing deformations of integrable cluster maps corresponding to the Dynkin types $A_{2N}$, lifting these to higher-dimensional maps possessing the Laurent property and demonstrating integrality of the deformations for $N\leq 3$. This provides the first infinite class of examples (in arbitrarily high rank) of such maps and gives information on the associated discrete integrable systems. Key to our approach is a ``local expansion'' operation on quivers which allows us to construct and study mutations in type $A_{2N}$ from those in type $A_{2(N-1)}$.
title Deformed cluster maps of type $A_{2N}$
topic Exactly Solvable and Integrable Systems
Dynamical Systems
Quantum Algebra
37J70 (Primary) 13F60, 39A36, 81R12 (Secondary)
url https://arxiv.org/abs/2402.18310