Deformed cluster maps of type A_2N

Grabowski, Jan and Hone, Andrew and Kim, Wookyung (2024) Deformed cluster maps of type A_2N. arxiv.org.

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Abstract

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≤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).