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Discrete mathematical modelling seminar
Seminar information archive ～04/23｜Next seminar｜Future seminars 04/24～
| Organizer(s) | Tetsuji Tokihiro, Ralph Willox |
|---|
2016/12/19
17:30-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Anton Dzhamay (University of Northern Colorado)
Discrete Painlevé equations on the affine A3 surface (ENGLISH)
Anton Dzhamay (University of Northern Colorado)
Discrete Painlevé equations on the affine A3 surface (ENGLISH)
[ Abstract ]
We explain how to construct the birational representation of the extended affine Weyl symmetry group D5 and consider examples of discrete Painlevé equations that correspond to certain translation elements in this group. One of the examples is the famous q-PV equation of Jimbo-Sakai. Some other examples are conjugated to it via explicit change of variables and we explain how representing translation elements as words in the group allows us to see the corresponding change of coordinates explicitly. We also show a new example of a discrete Painlevé equation that is elementary (short translation), but at the same time is different from the q-PVI equation.
We explain how to construct the birational representation of the extended affine Weyl symmetry group D5 and consider examples of discrete Painlevé equations that correspond to certain translation elements in this group. One of the examples is the famous q-PV equation of Jimbo-Sakai. Some other examples are conjugated to it via explicit change of variables and we explain how representing translation elements as words in the group allows us to see the corresponding change of coordinates explicitly. We also show a new example of a discrete Painlevé equation that is elementary (short translation), but at the same time is different from the q-PVI equation.
