The Minkowski sum of a zonotope and the Voronoi polytope of the root lattice E{sub 7}
- Central Economics and Mathematics Institute, RAS, Moscow (Russian Federation)
We show that the Minkowski sum P{sub V}(E{sub 7})+Z(U) of the Voronoi polytope P{sub V}(E{sub 7}) of the root lattice E{sub 7} and the zonotope Z(U) is a 7-dimensional parallelohedron if and only if the set U consists of minimal vectors of the dual lattice E{sub 7}{sup *} up to scalar multiplication, and U does not contain forbidden sets. The minimal vectors of E{sub 7} are the vectors r of the classical root system E{sub 7}. If the r{sup 2}-norm of the roots is set equal to 2, then the scalar products of minimal vectors from the dual lattice only take the values {+-}1/2. A set of minimal vectors is referred to as forbidden if it consists of six vectors, and the directions of some of these vectors can be changed so as to obtain a set of six vectors with all the pairwise scalar products equal to 1/2. Bibliography: 11 titles.
- OSTI ID:
- 22156587
- Journal Information:
- Sbornik. Mathematics, Journal Name: Sbornik. Mathematics Journal Issue: 11 Vol. 203; ISSN 1064-5616
- Country of Publication:
- United States
- Language:
- English
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