Spherical 2-Designs and Lattices from Abelian Groups

Authors

Albrecht Böttcher, Technische Universitat Chemnitz
Lenny Fukshansky, Claremont McKenna CollegeFollow
Stephan Ramon Garcia, Pomona CollegeFollow
Hiren Maharaj, Pomona College

Document Type

Article - preprint

Department

Mathematics (CMC), Mathematics (Pomona)

Publication Date

2015

Abstract

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.

Rights Information

© 2015 Böttcher, Fukshansky, Garcia, Maharaj

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Terms of Use for work posted in Scholarship@Claremont.

Recommended Citation

Boettcher, A., Fukshansky, L., Garcia, S., Maharaj, H., Spherical 2-designs and lattices from Abelian groups, preprint.