The elliptic quantum algebra $A_{q,p}(\widehat{s{l}_n})$ and its bosonization at level one

Abstract

We extend the work of Foda et al and propose an elliptic quantum algebra $A_{q,p}(\widehat{s{l}_n})$. Similar to the case of $A_{q,p}(\widehat{s{l}_2})$, our presentation of the algebra is based on the relation $RLL=LL{R}^{\ast }$, where $R$ and $R^{\ast }$ are $Z_n$ symmetric R-matrices with the elliptic moduli chosen differently and a factor is also involved. With the help of the results obtained by Asai et al, we realize type I and type II vertex operators in terms of bosonic free fields for $Z_n$ symmetric Belavin model. We also give a bosonization for the elliptic quantum algebra $A_{q,p}(\widehat{s{l}_n})$ at level one.

17 pages, Latex file 43k

References in corpus (3)

• Massless $XXZ$ Model and Degeneration of the Elliptic Algebra $A_{q,p}(\widehat{s{l}_2})$
• A $\hslash$-deformed Virasoro Algebra as Hidden Symmetry of the Restricted sine-Gordon Model
• Bosonization of vertex operators for Zn symmetric Belavin model and its correlation functions

Cited by in corpus (2)

• Type II vertex operators for the $A_{n-1}^{(1)}$ face model
• Vertex operator approach for form factors of Belavin's $(Z/nZ)$-symmetric model