Weyl groups of the fine gradings on $\e_6$

TL;DR

This paper determines the Weyl groups associated with the fine gradings on the exceptional Lie algebra _6, focusing on those with infinite universal grading groups, providing a detailed classification.

Contribution

It explicitly computes the Weyl groups for all fine gradings with infinite universal grading group on _6, a previously unclassified aspect.

Findings

Weyl groups for all relevant fine gradings are explicitly described.

Classification includes gradings with infinite universal grading groups.

Provides foundational data for symmetry analysis of _6.

Abstract

The Weyl groups of the fine gradings with infinite universal grading group on $\mathfrak{e}_6$ are given.