Exceptional complex Lie groups have become increasingly important in various fields of mathematics and physics. As a result, there has been interest in expanding the representation theory of finite groups to include embeddings into the exceptional Lie groups. Cohen, Griess, Lisser, Ryba, Serre and Wales have pioneered this area, classifying the finite simple and quasisimple subgroups that embed in the exceptional complex Lie groups.
This work contains the first major results concerning conjugacy classes of embeddings of finite subgroups of an exceptional complex Lie group in which there are large numbers of classes. The approach developed in this work is character theoretic, taking advantage of the classical subgroups of $E_8 (\mathbb C)$. The machinery used is relatively elementary and has been used by the author and others to solve other conjugacy problems. The results presented here are very explicit. Each known conjugacy class is listed by its fusion pattern with an explicit character afforded by an embedding in that class.
Dr. Frey has been at Cedarville since 1997. He has published numerous mathematics articles and has presented his research at mathematics conferences. He was a runner-up for the Sumner-Myers award for best math dissertation at the University of Michigan in 1995. Dr. Frey's has completed research concerning conjugacy of finite, perfect subgroups of exceptional complex Lie groups. He was invited to present his research in the summer of 2005 at the Ecole Polytechnique Federale in Lausanne, Switzerland.
Visit Dr. Frey's SelectedWorks page.
Available at: http://works.bepress.com/darrin_frey/17/