Exchange Relations for the q-Vertex Operators of $U_q(\widehat{sl2})$

TL;DR

This paper derives explicit solutions, connection matrices, and exchange relations for q-vertex operators of U_q(sl2), linking them to elliptic IRF models and advancing understanding of q-deformed conformal field theories.

Contribution

It provides explicit fundamental solutions and exchange relations for q-vertex operators of U_q(sl2), connecting them to elliptic IRF models and fusion procedures.

Findings

Explicit fundamental solutions for q-vertex operators

Connection matrices match elliptic IRF weights

Confirmed equivalence via fusion from ABF models

Abstract

We consider the q-deformed Knizhnik-Zamolodchikov equation for the two point function of q-deformed vertex operators of $U_q(sl_2^)$. We give explicitly the fundamental solutions, the connection matrices and the exchange relations for the q-vertex operators of spin 1/2 and $j \in {1\over 2}{\bf Z}_{\geq 0}$. Consequently, we confirm that the connection matrices are equivalent to the elliptic Boltzman weights of IRF type obtained by the fusion procedure from ABF models.