The character tables of centralizers in Weyl Groups of $E_6$, $E_7$, $F_4$, $G_2$

TL;DR

This paper computes the conjugacy class representatives and character tables of centralizers in Weyl groups of types E6, E7, F4, and G2 using GAP software, aiding classification of related Hopf algebras.

Contribution

It provides the first comprehensive character tables of centralizers in these specific Weyl groups, facilitating algebraic classification tasks.

Findings

Character tables of centralizers are fully determined.

Conjugacy class representatives are explicitly identified.

Results support classification of finite-dimensional pointed Hopf algebras.

Abstract

To classify the finite dimensional pointed Hopf algebras with Weyl group $G$ of $E_6$, $E_7$, $F_4$, $G_2$, we obtain the representatives of conjugacy classes of $G$ and all character tables of centralizers of these representatives by means of software GAP.