On The Construction of W(N)-Algebras In The Form Of A(N-1)-Casimir Algebras

TL;DR

This paper explores the construction of W(N)-algebras, demonstrating that their primary fields can be aligned with Casimir operators in terms of conformal spins and eigenvalues, revealing a deeper algebraic structure.

Contribution

It introduces a method to construct W(N)-algebras where primary fields share eigenvalues with Casimir operators, extending previous understanding of their algebraic relationships.

Findings

Existence of W(N)-algebras with primary fields matching Casimir eigenvalues.

Extension of the coincidence between conformal spins and Casimir operator orders.

Deeper insight into the algebraic structure of W(N)-algebras.

Abstract

Casimir W-algebras are shown to exist in such a way that the conformal spins of primary(generating) fields coincide with the orders of independent Casimir operators. We show here that this coincidence can be extended further to the case that these generating fields have the same eiginvalues with the Casimir operators.