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Discrete mathematical modelling seminar
Seminar information archive ～05/23｜Next seminar｜Future seminars 05/24～
| Organizer(s) | Tetsuji Tokihiro, Ralph Willox |
|---|
2024/12/26
15:00-17:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Wookyung KIM (Graduate School of Mathematical Sciences)
Integrable deformation of cluster map associated to finite type Dynkin diagram
Wookyung KIM (Graduate School of Mathematical Sciences)
Integrable deformation of cluster map associated to finite type Dynkin diagram
[ Abstract ]
An integrable deformation of a cluster map is an integrable Poisson map which is composed of a sequence of deformed cluster mutations, namely, parametric birational maps preserving the presymplectic form but destroying the Laurent property, which is a necessary part of the structure of a cluster algebra. However, this does not imply that the deformed map does not arise from a cluster map: one can use so-called Laurentification, which is a lifting of the map into a higher-dimensional space where the Laurent property is recovered, and thus the deformed map can be generated from elements in a cluster algebra. This deformation theory was introduced recently by Hone and Kouloukas, who presented several examples, including deformed integrable cluster maps associated with Dynkin types A_2,A_3 and A_4. In this talk, we will consider the deformation of integrable cluster map corresponding to the general even dimensional case, Dynkin type A_{2N}. If time permits, we will review the deformation of the cluster maps of other finite type cases such as type C and D. This is joint work with Grabowski, Hone and Mase.
An integrable deformation of a cluster map is an integrable Poisson map which is composed of a sequence of deformed cluster mutations, namely, parametric birational maps preserving the presymplectic form but destroying the Laurent property, which is a necessary part of the structure of a cluster algebra. However, this does not imply that the deformed map does not arise from a cluster map: one can use so-called Laurentification, which is a lifting of the map into a higher-dimensional space where the Laurent property is recovered, and thus the deformed map can be generated from elements in a cluster algebra. This deformation theory was introduced recently by Hone and Kouloukas, who presented several examples, including deformed integrable cluster maps associated with Dynkin types A_2,A_3 and A_4. In this talk, we will consider the deformation of integrable cluster map corresponding to the general even dimensional case, Dynkin type A_{2N}. If time permits, we will review the deformation of the cluster maps of other finite type cases such as type C and D. This is joint work with Grabowski, Hone and Mase.
