Fusion Rules for the q-deformed Vertex Operators of U_q(sl(2)^)

TL;DR

This paper investigates the properties of q-vertex operators in the quantum group U_q(sl(2)^), deriving fusion rules that determine when null vectors decouple, advancing understanding of their algebraic structure.

Contribution

It introduces the existence conditions for q-vertex operators in U_q(sl(2)^), providing new fusion rules that clarify their decoupling properties.

Findings

Derived the existence conditions for q-vertex operators.

Established fusion rules for null vector decoupling.

Enhanced understanding of q-vertex operator algebra.

Abstract

We analyze the properties of the q-vertex operators of U_q(sl(2)^) introduced by Frenkel and Reshetikhin. As the condition for the null vector decoupling, we derive the existence condition of the q-vertex operators ( the fusion rules ).