Singular vectors by Fusions in affine su(2)

TL;DR

This paper derives explicit formulas for singular vectors in affine su(2) representations using fusion techniques from conformal field theory, enhancing understanding of their structure.

Contribution

It provides the first explicit expressions for singular vectors in affine su(2) highest weight modules via fusion formalism.

Findings

Explicit singular vector formulas derived

Fusion formalism applied to affine su(2)

Advances in representation theory understanding

Abstract

Explicit expressions for the singular vectors in the highest weight representations of $A_1^{(1)}$ are obtained using the fusion formalism of conformal field theory.