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Commutative Families of the Elliptic Macdonald Operator
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2014, том 10
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Commutative Families of the Elliptic Macdonald Operator
Інший ID:
2010 Mathematics Subject Classification: 17B37; 33D52
DOI:10.3842/SIGMA.2014.021
DOI:10.3842/SIGMA.2014.021
Посилання:
Commutative Families of the Elliptic Macdonald Operator / Y. Saito // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 8 назв. — англ.
Підтримка:
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.
Дата:
2014
Переглядів:
541
Завантажень:
249
Анотація:
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.
