Determinants of Lattices induced by Rational Subspaces
Peter McMullen · Bulletin of the London Mathematical Society · 1984
Let L and L ¯ be orthogonal complementary rational linear subspaces of En, and let Λ = L ∩ Zn and Λ ¯ = L ¯ ∩ Zn be the sublattices of the usual integer lattice Zn induced by L and L ¯ . Then the determinants of Λ and Λ are equal. The same relationship holds between the determinants of the lattices ∏ and ∏ obtained by orthogonal projection of Zn on to L and L ¯ .