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- Title
Contact Vectors of Point Lattices.
- Authors
Grishukhin, V. P.
- Abstract
The contact vectors of a lattice are vectors which are minimal in the -norm in their parity class. It is shown that, in the space of all symmetric matrices, the set of all contact vectors of the lattice defines the subspace containing the Gram matrix of the lattice . The notion of extremal set of contact vectors is introduced as a set for which the space is one-dimensional. In this case, the lattice is rigid. Each dual cell of the lattice is associated with a set of contact vectors contained in it. A dual cell is extremal if its set of contact vectors is extremal. As an illustration, we prove the rigidity of the root lattice for and the lattice dual to the root lattice .
- Subjects
RIESZ spaces; SYMMETRIC spaces
- Publication
Mathematical Notes, 2023, Vol 113, Issue 5/6, p642
- ISSN
0001-4346
- Publication type
Article
- DOI
10.1134/S0001434623050048