2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/187232The 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.12 pages, LaTeX 2eHigh Energy Physics - Theorytext