Explicit determination of a 727-dimensional root space of the hyperbolic   Lie algebra $E_{10}$
  The 727-dimensional root space associated with the level-2 root $\bLambda_1$ of the hyperbolic Kac--Moody algebra $E_{10}$ is determined using a recently developed string theoretic approach to hyperbolic algebras. The explicit form of the basis reveals a complicated structure with transversal as well as longitudinal string states present. 
Oliver B\"arwald (Hamburg University), Reinhold W. Gebert (IAS,   Princeton)