Commutative Families of the Elliptic Macdonald Operator
In the paper [J. Math. Phys. 50 (2009), 095215, 42 pages], Feigin, Hashizume, Hoshino, Shiraishi, and Yanagida constructed two families of commuting operators which contain the Macdonald operator (commutative families of the Macdonald operator). They used the Ding-Iohara-Miki algebra and the trigono...
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| Дата: | 2014 |
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| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2014
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/146833 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Commutative Families of the Elliptic Macdonald Operator / Y. Saito // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 8 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1468332019-02-12T01:25:29Z Commutative Families of the Elliptic Macdonald Operator Saito, Y. In the paper [J. Math. Phys. 50 (2009), 095215, 42 pages], Feigin, Hashizume, Hoshino, Shiraishi, and Yanagida constructed two families of commuting operators which contain the Macdonald operator (commutative families of the Macdonald operator). They used the Ding-Iohara-Miki algebra and the trigonometric Feigin-Odesskii algebra. In the previous paper [arXiv:1301.4912], the present author constructed the elliptic Ding-Iohara-Miki algebra and the free field realization of the elliptic Macdonald operator. In this paper, we show that by using the elliptic Ding-Iohara-Miki algebra and the elliptic Feigin-Odesskii algebra, we can construct commutative families of the elliptic Macdonald operator. In Appendix, we will show a relation between the elliptic Macdonald operator and its kernel function by the free field realization. 2014 Article Commutative Families of the Elliptic Macdonald Operator / Y. Saito // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 8 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 17B37; 33D52 DOI:10.3842/SIGMA.2014.021 http://dspace.nbuv.gov.ua/handle/123456789/146833 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
In the paper [J. Math. Phys. 50 (2009), 095215, 42 pages], Feigin, Hashizume, Hoshino, Shiraishi, and Yanagida constructed two families of commuting operators which contain the Macdonald operator (commutative families of the Macdonald operator). They used the Ding-Iohara-Miki algebra and the trigonometric Feigin-Odesskii algebra. In the previous paper [arXiv:1301.4912], the present author constructed the elliptic Ding-Iohara-Miki algebra and the free field realization of the elliptic Macdonald operator. In this paper, we show that by using the elliptic Ding-Iohara-Miki algebra and the elliptic Feigin-Odesskii algebra, we can construct commutative families of the elliptic Macdonald operator. In Appendix, we will show a relation between the elliptic Macdonald operator and its kernel function by the free field realization. |
| format |
Article |
| author |
Saito, Y. |
| spellingShingle |
Saito, Y. Commutative Families of the Elliptic Macdonald Operator Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Saito, Y. |
| author_sort |
Saito, Y. |
| title |
Commutative Families of the Elliptic Macdonald Operator |
| title_short |
Commutative Families of the Elliptic Macdonald Operator |
| title_full |
Commutative Families of the Elliptic Macdonald Operator |
| title_fullStr |
Commutative Families of the Elliptic Macdonald Operator |
| title_full_unstemmed |
Commutative Families of the Elliptic Macdonald Operator |
| title_sort |
commutative families of the elliptic macdonald operator |
| publisher |
Інститут математики НАН України |
| publishDate |
2014 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/146833 |
| citation_txt |
Commutative Families of the Elliptic Macdonald Operator / Y. Saito // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 8 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT saitoy commutativefamiliesoftheellipticmacdonaldoperator |
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2023-05-20T17:25:45Z |
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2023-05-20T17:25:45Z |
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1796153271454269440 |