A Variation of the q-Painlevé System with Affine Weyl Group Symmetry of Type E₇⁽¹⁾
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 syste...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2017 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2017
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/149269 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862650377781903360 |
|---|---|
| author | Nagao, H. |
| author_facet | Nagao, H. |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
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| first_indexed | 2025-12-01T16:54:43Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149269 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-01T16:54:43Z |
| publishDate | 2017 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Nagao, H. 2019-02-19T19:33:11Z 2019-02-19T19:33:11Z 2017 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. 1815-0659 2010 Mathematics Subject Classification: 14H70; 33D15; 33D70; 34M55; 37K20; 39A13; 41A21 DOI:10.3842/SIGMA.2017.092 https://nasplib.isofts.kiev.ua/handle/123456789/149269 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. 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). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications A Variation of the q-Painlevé System with Affine Weyl Group Symmetry of Type E₇⁽¹⁾ Article published earlier |
| spellingShingle | A Variation of the q-Painlevé System with Affine Weyl Group Symmetry of Type E₇⁽¹⁾ Nagao, H. |
| title | A Variation of the q-Painlevé System with Affine Weyl Group Symmetry of Type E₇⁽¹⁾ |
| title_full | A Variation of the q-Painlevé System with Affine Weyl Group Symmetry of Type E₇⁽¹⁾ |
| title_fullStr | A Variation of the q-Painlevé System with Affine Weyl Group Symmetry of Type E₇⁽¹⁾ |
| title_full_unstemmed | A Variation of the q-Painlevé System with Affine Weyl Group Symmetry of Type E₇⁽¹⁾ |
| title_short | A Variation of the q-Painlevé System with Affine Weyl Group Symmetry of Type E₇⁽¹⁾ |
| title_sort | variation of the q-painlevé system with affine weyl group symmetry of type e₇⁽¹⁾ |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149269 |
| work_keys_str_mv | AT nagaoh avariationoftheqpainlevesystemwithaffineweylgroupsymmetryoftypee71 AT nagaoh variationoftheqpainlevesystemwithaffineweylgroupsymmetryoftypee71 |