Coxeter Graphs for Super Weyl Groups of Exceptional Classical Lie Superalgebras

TL;DR

This paper determines the Coxeter graphs for super Weyl groups of exceptional classical Lie superalgebras, confirming previous proposals and advancing understanding of their structure.

Contribution

It provides explicit Coxeter graphs for super Weyl groups of exceptional Lie superalgebras, verifying earlier conjectures and presenting fundamental systems.

Findings

Coxeter graphs for super Weyl groups of $D(2,1, ext{alpha})$, $F(4)$, and $G(3)$ are explicitly constructed.

Verification of a prior proposal on Coxeter graphs for these super Weyl groups.

Fundamental systems of the exceptional Lie superalgebras are presented.

Abstract

Super Weyl group plays an important role in the study of representations of basic classical Lie superalgebras. The Coxeter graphs for super Weyl groups of basis classical Lie superalgebras have been given in \cite{CLS}, where the authors also made a proposal on the Coxeter graphs for the super Weyl groups of exceptional classical Lie superalgebras $D(2,1,\alpha)$, $F(4)$ and $G(3)$. In this paper, we present all fundamental systems of the exceptional Lie superalgebras and get the Coxeter graphs for the corresponding super Weyl groups, verifying a proposal in \cite{CLS}.