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Symmetric groups and lattices. (English) Zbl 1132.11329

Summary: This paper deals with various problems in lattice theory involving local extrema. In particular, we construct infinite series of highly symmetric spherical 3-designs which include some of the examples constructed by J. Martinet and B. Venkov [in: Euclidean lattices, spherical designs and modular forms. On the works of Boris Venkov. Monogr. Enseign. Math. 37, 112–134 (2001; Zbl 1131.11344)] in dimensions 5 and 7. We also construct new types of dual-extreme lattices.

MSC:

11H55 Quadratic forms (reduction theory, extreme forms, etc.)
11H56 Automorphism groups of lattices

Citations:

Zbl 1131.11344
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