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

TL;DR

This paper computes and lists the character tables of centralizers in the Weyl group of E8 to aid classification of certain Hopf algebras, using computational tools.

Contribution

It provides the first extensive list of character tables for centralizers in the Weyl group of E8, facilitating algebraic classification tasks.

Findings

Character tables of 28 centralizers in the Weyl group of E8 are provided.

The classification aids in understanding finite dimensional pointed Hopf algebras.

Computations were performed using GAP software.

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 1-- 28.