Fusion and singular vectors in A1{(1)} highest weight cyclic modules

TL;DR

This paper explores the relationship between fusion formalism and the Knizhnik--Zamolodchikov equation to derive explicit formulas for singular vectors in highest weight modules of A1{(1)}.

Contribution

It provides new explicit formulas for singular vectors in A1{(1)} highest weight modules using conformal field theory techniques.

Findings

Derived explicit formulas for singular vectors

Linked fusion formalism with KZ equations

Enhanced understanding of A1{(1)} modules

Abstract

We show how the interplay between the fusion formalism of conformal field theory and the Knizhnik--Zamolodchikov equation leads to explicit formulae for the singular vectors in the highest weight representations of A1{(1)}.