Dynamically twisted algebra $A_{q,p;\hat{\pi}}(\hat{gl_2})$ as current algebra generalizing screening currents of q-deformed Virasoro algebra

Abstract

In this paper, we propose an elliptic algebra $A_{q,p;\hat{\pi}}(\hat{gl_2})$ which is based on the relations $RLL=LLR^{*}$, where $R$ and $R^{*}$ 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 $A_{q,p;\hat{\pi}}(\hat{gl_2})$ is related with the algebra $A_{q,p}(\hat{gl_2})$ by a dynamically twisting.