Article - preprint
Mathematics (CMC), Mathematics (Pomona)
We consider lattices generated by finite Abelian groups. The main result says that such a lattice is strongly eutactic, which means the normalized minimal vectors of the lattice form a spherical 2-design, if and only if the group is of odd order or if it is a power of the group of order 2. This result also yields a criterion for the appropriately normalized minimal vectors to constitute a uniform normalized tight frame.
© 2015 Böttcher, Fukshansky, Garcia, Maharaj
Boettcher, A., Fukshansky, L., Garcia, S., Maharaj, H., Spherical 2-designs and lattices from Abelian groups, preprint.