Dynamically twisted algebra $A_{q,p;\hat{\pi }}(\widehat{g{l}_2})$ as current algebra generalizing screening currents of q-deformed Virasoro algebra

Abstract

In this paper, we propose an elliptic algebra $A_{q,p;\hat{\pi }}(\widehat{g{l}_2})$ which is based on the relations $RLL=LL{R}^{\ast }$, where $R$ and $R^{\ast }$ are the dynamical R-maxtrices of $A_1^{(1)}$ type face model with the elliptic moduli shifted by the center of the algebra. From the Ding-Frenkel correspondence, we find that its corresponding (Drinfeld) current algebra at level one is the algebra of screening currents for q-deformed Virasoro algebra.We realize the elliptic algebra at level one by Miki's construction from the bosonization for the type I and type II vertex operators.We also show that the algebra $A_{q,p;\hat{\pi }}(\widehat{g{l}_2})$ is related with the algebra $A_{q,p}(\widehat{g{l}_2})$ by a dynamically twisting.

24 pages, Latex file 66K

References in corpus (1)

• A $\hslash$-deformation of the $W_N$ algebra and its vertex operators

Cited by in corpus (2)

• Infinite Hopf family of elliptic algebras and bosonization
• Affine A^{(1)}_{3} N=2 monopole as the D module and affine ADHMN sheaf