Double Vogan superdiagrams of Lie superalgebras and symmetric superspaces

TL;DR

This paper introduces double Vogan superdiagrams, a new graphical tool for classifying pairs of commuting involutions on complex simple Lie superalgebras, aiding in the classification of symmetric superpairs.

Contribution

The paper presents the concept of double Vogan superdiagrams, extending existing diagrams to classify pairs of involutions and symmetric superpairs in Lie superalgebras.

Findings

Double Vogan superdiagrams correspond to pairs of commuting involutions.

They provide an independent classification of symmetric superpairs.

The method enhances understanding of real forms of Lie superalgebras.

Abstract

A Vogan superdiagram is a set of involution and painting on a Dynkin diagram. It selects a real form, or equivalently an involution, from a complex simple Lie superalgebra. We introduce the double Vogan superdiagram, which is two sets of Vogan superdiagrams superimposed on an affine Dynkin diagram. They correspond to pairs of commuting involutions on complex simple Lie superalgebras, and therefore provide an independent classification of the simple locally symmetric or symmetric superpairs.