Miura-Like Free Field Realization Of Fermionic Casimir WB(3) Algebras

TL;DR

This paper constructs explicit free field realizations of the fermionic Casimir WB(3) algebra using a quantum Miura-like transformation, demonstrating its closure and associativity for all central charges.

Contribution

It provides a new explicit construction of the WB(3) algebra with fermionic fields, extending the understanding of Casimir W algebras for non simply-laced Lie types.

Findings

WB(3) algebra is closed and associative for all central charges

Explicit free field realization of fermionic Casimir WB(3) algebra

Extension of quantum Miura transformation to non simply-laced cases

Abstract

Starting from the well-known quantum Miura-like transformation for the non simply-laced Lie algebras B(3),we give an explicit construction of the Casimir WB(3) algebras.We reserve the notation WB(N) for the Casimir W algebras of type W(2,4,6,...,2N,N+1/2) which contains one fermionic field. It is seen that WB(3) algebra is closed an associative for all values of the central element c.