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A Variation of the q-Painlevé System with Affine Weyl Group Symmetry of Type E₇⁽¹⁾
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2017, том 13
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A Variation of the q-Painlevé System with Affine Weyl Group Symmetry of Type E₇⁽¹⁾
Інший ID:
2010 Mathematics Subject Classification: 14H70; 33D15; 33D70; 34M55; 37K20; 39A13; 41A21
DOI:10.3842/SIGMA.2017.092
DOI:10.3842/SIGMA.2017.092
Посилання:
A Variation of the q-Painlevé System with Affine Weyl Group Symmetry of Type E₇⁽¹⁾ / H. Nagao // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 50 назв. — англ.
Підтримка:
The author shall be thankful to Professor Yasuhiko Yamada for valuable discussions. The author
is also grateful to the referees for stimulating comments. This work was partially supported by
Expenses Revitalizing Education and Research of Akashi College (0217030).
Дата:
2017
Переглядів:
591
Завантажень:
241
Анотація:
Recently a certain q-Painlevé type system has been obtained from a reduction of the q-Garnier system. In this paper it is shown that the q-Painlevé type system is associated with another realization of the affine Weyl group symmetry of type E₇⁽¹⁾ and is different from the well-known q-Painlevé system of type E₇⁽¹⁾ from the point of view of evolution directions. We also study a connection between the q-Painlevé type system and the q-Painlevé system of type E₇⁽¹⁾. Furthermore determinant formulas of particular solutions for the q-Painlevé type system are constructed in terms of the terminating q-hypergeometric function.
