New ${\mathcal{W}}_{q,p}(sl(2))$ algebras from the elliptic algebra ${\mathcal{A}}_{q,p}(\hat{s}l(2{)}_c)$

Abstract

We construct operators t(z) in the elliptic algebra introduced by Foda et al. ${\mathcal{A}}_{q,p}(\hat{s}l(2{)}_c)$. They close an exchange algebra when p^m=q^{c+2} for m integer. In addition they commute when p=q^{2k} for k integer non-zero, and they belong to the center of ${\mathcal{A}}_{q,p}(\hat{s}l(2{)}_c)$ when k is odd. The Poisson structures obtained for t(z) in these classical limits are identical to the q-deformed Virasoro Poisson algebra, characterizing the exchange algebras at generic values of p, q and m as new ${\mathcal{W}}_{q,p}(sl(2))$ algebras.

9 pages; Warning: LaTeX2e Document - packages subeqn,amsfonts

References in corpus (3)

• Algebra of screening operators for the deformed $W_n$ algebra
• Elliptic algebra $A_{q,p}(\widehat{s{l}_2})$ in the scaling limit
• Poisson structures on the center of the elliptic algebra A_{p,q}(sl(2)_c)

Cited by in corpus (5)

• From finite geometry exact quantities to (elliptic) scattering amplitudes for spin chains: the 1/2-XYZ
• Central extensions of classical and quantum q-Viraroso algebras
• Deformed Virasoro algebras from elliptic quantum algebras
• Deformed Double Yangian Structures
• q-deformed W-algebras and elliptic algebras