Deformed cluster maps of type $A_{2N}$
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911587071164416 |
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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 |
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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 |