ISSN:
1572-9036
Keywords:
integral system
;
root system
;
lattice
;
polytope
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract We consider uniform odd systems, i.e. sets of vectors of constant odd norm with odd inner product, and the lattice L(V) linearly generated by a uniform odd system V of odd norm 2t+1. If uu ≡ p (mod 4) for all u ∈ V, one has v2 ≡ p (mod 4) if v2 is odd and v2 ≡ 0 (mod 4) if v2 is even, for any vector v ∈ L(V). The vectors of even norm form a double even sublattice L0(V) of L(V), i.e. $$(1/\sqrt 2 )L_0 (\mathcal{V}) $$ is an even lattice. The closure of V, i.e. all vectors of L(V) of norm 2t+1, are minimal vectors of L(V) for t=1, and they are almost always minimal for t=2. For such t, the convex hull of vectors of the closure of V is an L-polytope of L0V and the contact polytope of L(V). As an example, we consider closed uniform odd systems of norm 5 spanning equiangular lines.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1005994621749
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