Defining relations for W-algebras from singular vectors

TL;DR

This paper demonstrates how the fundamental relations of W-algebras can be derived directly from the singular vectors of specific highest weight representations, providing a new approach to understanding their structure.

Contribution

It introduces a method to recover W-algebra relations from singular vectors, offering a novel perspective on their algebraic structure.

Findings

W-algebra relations can be derived from singular vectors

Singular vectors encode the algebraic structure of W-algebras

New approach simplifies understanding of W-algebra commutation relations

Abstract

It is shown that the commutation relations of W-algebras can be recovered from the singular vectors of their simplest nontrivial, completely degenerate highest weight representation.