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Conjugacy of Embeddings of Alternating Groups in Exceptional Lie Groups
by Darrin Frey   Alex Ryba

Vol. 13 No. 4 (2018) P.463~P.480
 DOI: https://doi.org/10.21915/BIMAS.2018406 10.21915/BIMAS.2018406

ABSTRACT

We discuss conjugacy classes of embeddings of Alternating groups in Exceptional Lie groups. We settle the count of classes of embeddings in $E_8$ of a subgroup $Alt_10$ and its double cover. This involves computation and the reduction of the problems to relative eigenvector problems. We update previously published tables of embeddings. We comment on the improvements present in our table and on the remaining unsettled conjugacy questions.

KEYWORDS
Alternating group, Exceptional Group of Lie type, Relative Eigenvector.

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 20D06, 20E28

MILESTONES