Let [A 1 , ..., A m ] be a set of m matrices of size n\_n over the field F such that A i # SL(n, F) for 1 i m and such that A i &A j # SL(n, F) for 1 i< j m. The largest integer m for which such a set exists is called the Parsons number for n and F, denoted m(n, F). We will call such a set of m(n, F
Conference Matrices and Unimodular Lattices
β Scribed by Robin Chapman
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 147 KB
- Volume
- 22
- Category
- Article
- ISSN
- 0195-6698
No coin nor oath required. For personal study only.
β¦ Synopsis
Conference matrices are used to define complex structures on real vector spaces. Certain lattices in these spaces become modules for rings of quadratic integers. Multiplication of these lattices by nonprincipal ideals yields simple constructions of further lattices including the Leech lattice.
π SIMILAR VOLUMES
## Abstract Conditions for a matrix to be totally unimodular, due to Camion, are applied to extend and simplify proofs of other characterizations of total unimodularity.
It is shown that an n-dimensional unimodular lattice has minimal norm at most 2[nΓ24]+2, unless n=23 when the bound must be increased by 1. This result was previously known only for even unimodular lattices. Quebbemann had extended the bound for even unimodular lattices to strongly N-modular even la
It is known that the symplectic group Sp p has two complex conjugate 2 n n Ε½ . Ε½ . irreducible representations of degree p q 1 r2 realized over β«ήβ¬ y p , provided ' that p ' 3 mod 4. In the paper we give an explicit construction of an odd unimodu-Ε½ . Ε½ . n n lar Sp p ΠΈ 2-invariant lattice β¬ p, n in