Elliptic Ding-Iohara algebra and the free field realization of the elliptic Macdonald operator (Q473121)

Summary: The Ding-Iohara algebra is a quantum algebra arising from the free field realization of the Macdonald operator. Starting from the elliptic kernel function introduced by Komori, Noumi and Shiraishi [\textit{Y. Komori} et al., SIGMA, Symmetry Integrability Geom. Methods Appl. 5, Paper 054, 40 p. (2009; Zbl 1160.81393)], we define an elliptic analog of the Ding-Iohara algebra. The free field realization of the elliptic Macdonald operator is also constructed.