We work out the decomposition of the indefinite Kac Moody algebras ${ E_{ 10}}$ and ${ E_{ 11}}$ w.r.t. their respective subalgebras $A_9$ and $A_{ 10}$ at low levels. Tables of the irreducible representations with their outer multiplicities are presented for ${ E_{ 10}}$ up to level $\ell = 18$ and for ${ E_{ 11}}$ up to level $\ell =10$. On the way we confirm and extend existing results for ${ E_{ 10}}$ root multiplicities, and for the first time compute non-trivial root multiplicities of ${ E_{ 11}}$.
Categories: hep-th math.QA