Null vectors of the $WBC_2$ algebra

TL;DR

This paper derives explicit null vectors for the c algebra's highest weight representations, generalizing known Virasoro and $W_3$ null vectors, and links quantum Toda models with fusion methods.

Contribution

It provides explicit formulas for null vectors of the c algebra, extending previous results for Virasoro and $W_3$ algebras, and connects quantum Toda models to fusion techniques.

Findings

Explicit null vectors for c algebra derived

Connection established between quantum Toda models and fusion method

Generalization of Virasoro and $W_3$ null vectors

Abstract

Using the fusion principle of Bauer et al. we give explicit expressions for some null vectors in the highest weight representations of the \bc algebra in two different forms. These null vectors are the generalization of the Virasoro ones described by Benoit and Saint-Aubin and analogues of the $W_3$ ones constructed by Bowcock and Watts. We find connection between quantum Toda models and the fusion method.