
SIGMA 10 (2014), 021, 17 pages arXiv:1305.7097
https://doi.org/10.3842/SIGMA.2014.021
Contribution to the Special Issue in honor of Anatol Kirillov and Tetsuji Miwa
Commutative Families of the Elliptic Macdonald Operator
Yosuke Saito
Mathematical Institute of Tohoku University, Sendai, Japan
Received October 01, 2013, in final form February 25, 2014; Published online March 11, 2014
Abstract
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 DingIoharaMiki algebra and the trigonometric FeiginOdesskii algebra.
In the previous paper [arXiv:1301.4912], the present author constructed the elliptic DingIoharaMiki algebra and the free field
realization of the elliptic Macdonald operator.
In this paper, we show that by using the elliptic DingIoharaMiki algebra and the elliptic FeiginOdesskii 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.
Key words:
elliptic DingIoharaMiki algebra; free field realization; elliptic Macdonald operator.
pdf (401 kb)
tex (16 kb)
References
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