Orbits in lattices (Q6613263)

Let \(L\) be a lattice and let \(O(L)\) be the orthogonal group. The author develops algorithms to find orbits of vectors for certain subgroups of \(O(L)\), which can be applied to determine efficient representations of Fourier series of modular forms for \(O(2,n).\) He develops algorithms for calculating Tits builds of subgroups of \(O(L)\) for a lattice of signature \((2,n)\). He describes how these algorithms can determine the configuration of boundary components in the Baily-Borel compactification of orthogonal modular varieties. Finally, he uses these algorithms to calculate Tits building for certain examples.