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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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2014 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2014
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/146833 |
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| Cite this: | 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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Saito, Y. 2019-02-11T16:43:57Z 2019-02-11T16:43:57Z 2014 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 https://nasplib.isofts.kiev.ua/handle/123456789/146833 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. This paper is a contribution to the Special Issue in honor of Anatol Kirillov and Tetsuji Miwa. The full collection is available at http://www.emis.de/journals/SIGMA/InfiniteAnalysis2013.html. The author would like to thank Koji Hasegawa and Gen Kuroki for helpful discussions and comments. The author also would like to thank referees for their valuable comments on improvements of the present paper. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Commutative Families of the Elliptic Macdonald Operator Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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| title |
Commutative Families of the Elliptic Macdonald Operator |
| spellingShingle |
Commutative Families of the Elliptic Macdonald Operator Saito, Y. |
| 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 |
| author |
Saito, Y. |
| author_facet |
Saito, Y. |
| publishDate |
2014 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
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Article |
| 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.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.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. |
| work_keys_str_mv |
AT saitoy commutativefamiliesoftheellipticmacdonaldoperator |
| first_indexed |
2025-12-07T19:24:57Z |
| last_indexed |
2025-12-07T19:24:57Z |
| _version_ |
1850878719843893248 |