TY - JOUR

T1 - Deformed cluster maps of type A_2N

AU - Grabowski, Jan

AU - Hone, Andrew

AU - Kim, Wookyung

PY - 2024/2/28

Y1 - 2024/2/28

N2 - 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).

AB - 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).

M3 - Journal article

JO - arxiv.org

JF - arxiv.org

ER -