Elliptic algebra $A_{q,p}(\hat{sl_2})$ in the scaling limit

Abstract

The scaling limit $A_{\hbar,\eta}(\hat{sl_2})$ of the elliptic algebra $A_{q,p}(\hat{sl_2})$ is investigated. The limiting algebra is defined in terms of a continuous family of generators being Fourier harmonics of Gauss coordinates of the $L$-operator. Ding-Frenkel isomorphism between $L$-operator's and current descriptions of the algebra $A_{\hbar,\eta}(\hat{sl_2})$ is established and is identified with the Riemann problem on a strip. The representations, coalgebraic structure and intertwining operators of the algebra are studied.