Modular curves, invariant theory and $E_8$

Abstract

The $E_8$ root lattice can be constructed from the modular curve $X(13)$ by the invariant theory for the simple group $\text{PSL}(2,13)$. This gives a different construction of the $E_8$ root lattice. It also gives an explicit construction of the modular curve $X(13)$.

39 pages. arXiv admin note: text overlap with arXiv:1511.05278