The character tables of centralizers in Weyl Group of $E_8$ III

TL;DR

This paper provides character tables of centralizers in the Weyl group of E8, aiding the classification of certain Hopf algebras, by computing representatives and character tables using GAP software.

Contribution

It offers the explicit character tables of centralizers in the Weyl group of E8, focusing on tables 47-64, which were previously unlisted.

Findings

Character tables for centralizers 47-64 are computed and listed.

The classification of finite-dimensional pointed Hopf algebras with Weyl group E8 is advanced.

Software GAP is used effectively for these computations.

Abstract

To classify the finite dimensional pointed Hopf algebras with Weyl group $G$ of $E_8$, we obtain the representatives of conjugacy classes of $G$ and all character tables of centralizers of these representatives by means of software GAP. In this paper we only list character table 47--64.