Classification of positive forms having prescribed automorphisms. (English) Zbl 0951.11024

Kim, Myung-Hwan (ed.) et al., Integral quadratic forms and lattices. Proceedings of the international conference on integral quadratic forms and lattices, Seoul National University, Seoul, Korea, June 15-19, 1998. Dedicated to the memory of Dennis Ray Estes. Providence, RI: American Mathematical Society. Contemp. Math. 249, 199-204 (1999).
For a finite integral matrix group \(G\), the author and J. Martinet [Enseign. Math., II. Sér. 41, 335-365 (1995; Zbl 0848.52006)] have introduced a cellular decomposition of the set of positive definite \(G\)-invariant quadratic forms of minimum 1. Two forms belong to the same cell if they have the same minimal vectors; up to \(G\)-equivalence only finitely many bounded cells exist. After stating a “mass formula with signs” for such cells, the paper discusses the case of the regular representation of a cyclic group. Up to order 5 the cells are completely enumerated.
For the entire collection see [Zbl 0931.00029].


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


Zbl 0848.52006