On the free field realization of $WBC_n$ algebras

TL;DR

This paper presents a classical free field realization of $WBC_n$ algebras, providing explicit generators that remain unchanged upon quantization, advancing understanding of their algebraic structure.

Contribution

It introduces a new classical free field realization for $WBC_n$ algebras and explicitly constructs their generators in a compact form.

Findings

Explicit classical generators for $WBC_n$ algebras derived

Generators remain unchanged under quantization

Provides a compact form for arbitrary $WBC_n$ algebras

Abstract

Defining the $WBC_n$ algebras as the commutant of certain screening charges a special form for the classical generators is obtained which does not change under quantisation. This enables us to give explicitly the first few generators in a compact form for arbitrary $WBC_n$ algebras.