Reduction mod. 2 of del Pezzo lattices

Abstract

For an even lattice L , the form v --> (v.v)/2 induces a quadratic form q on the (Z/2)-vector space L/2L . For the lattices associated to some particular root systems, we show that reduction mod. 2 induces a bijection between the roots of L and the vectors of L/2L with q=1 , and an isomorphism of O(L)/<-1> onto O(L/2L).