Elliptic algebra $A_{q,p}(\widehat{s{l}_2})$ in the scaling limit

Abstract

The scaling limit $A_{\hslash ,\eta }(\widehat{s{l}_2})$ of the elliptic algebra $A_{q,p}(\widehat{s{l}_2})$ 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 $A_{\hslash ,\eta }(\widehat{s{l}_2})$ is established and is identified with the Riemann problem on a strip. The representations, coalgebraic structure and intertwining operators of the algebra are studied.

Latex 2.09, 3 fig. under bezier.sty, macros uses AMS fonts, 27 pages

Cited by in corpus (11)

• Form-factors of exponential fields in the affine A^{(1)}_{N-1} Toda model
• The elliptic algebra U_{q,p}(\hat{sl}_N) and the Drinfeld realization of the elliptic quantum group B_{q,λ}(\hat{sl}_N)
• Poisson structures on the center of the elliptic algebra A_{p,q}(sl(2)_c)
• New ${\mathcal{W}}_{q,p}(sl(2))$ algebras from the elliptic algebra ${\mathcal{A}}_{q,p}(\hat{s}l(2{)}_c)$
• Factorization of the Universal R-matrix for $U_q({\widehat{sl}}_2)$
• Cladistics of Double Yangians and Elliptic Algebras
• The Drinfeld Realization of the Elliptic Quantum Group B_{q,lambda}(A_2^(2))
• Yangian Algebras and Classical Riemann Problems
• Classical elliptic current algebras
• On the Quasi-Hopf structure of deformed double Yangians
• Deformed Double Yangian Structures