Branching rule decomposition of the level-1 $E_8^{(1)}$-module with respect to the irregular subalgebra $F_4^{(1)}\oplus G_2^{(1)}$

Joshua D. Carey

Given a Lie algebra of type $E_8$, one can use Dynkin diagram automorphisms of the $E_6$ and $D_4$ Dynkin diagrams to locate a subalgebra of type $F_4\oplus G_2$. These automorphis…