Characteristic Dynkin diagrams and W-algebras

TL;DR

This paper classifies characteristic Dynkin diagrams for classical Lie algebras and explores their connection to W-algebras from non-Abelian Toda models, offering new insights into W algebra structures.

Contribution

It provides a systematic classification of characteristic Dynkin diagrams for A, B, C, D algebras and links this to the structure of W-algebras from Toda models.

Findings

Classification of characteristic Dynkin diagrams for classical Lie algebras.

Connection established between Dynkin diagrams and W-algebras.

Potential new insights into W algebra structures.

Abstract

We present a classification of characteristic Dynkin diagrams for the $A_N$, $B_N$, $C_N$ and $D_N$ algebras. This classification is related to the classification of \cw(\cg,\ck) algebras arising from non-Abelian Toda models, and we argue that it can give new insight on the structure of $W$ algebras.