Vertex Operator Extension of Casimir W A(N) Algebras

TL;DR

This paper extends Casimir $ ext{WA}_N$ algebras by incorporating a vertex operator related to non-simple roots of $A_{N-1}$, enriching the algebraic structure.

Contribution

It introduces a novel extension of Casimir $ ext{WA}_N$ algebras with vertex operators tied to non-simple roots, advancing algebraic understanding.

Findings

Extended $ ext{WA}_N$ algebras with new vertex operators

Enhanced algebraic structures involving non-simple roots

Potential applications in mathematical physics

Abstract

We give an extension of Casimir of Casimir $\cal{WA_N}$ algebras including a vertex operator which depends on non-simple roots of $A_{N-1}$.