Affine Vogan Diagrams and Symmetric Pairs

TL;DR

This paper introduces affine Vogan diagrams for complex simple Lie algebras, generalizing Vogan diagrams, and uses them to analyze involutions and symmetric pairs, including associated and symplectic types.

Contribution

The paper develops affine Vogan diagrams and demonstrates their application in classifying involutions and symmetric pairs in complex simple Lie algebras.

Findings

Affine Vogan diagrams are effective in representing involutions.

Application to symmetric pairs clarifies their structure.

Provides a new tool for studying complex Lie algebra symmetries.

Abstract

We introduce the affine Vogan diagrams of complex simple Lie algebras. These are generalizations of Vogan diagrams, and we study the involutions represented by them. We apply these diagrams to study the symmetric pairs, in particular the associated and symplectic symmetric pairs.