Abstract
An explicit description of a Dirichlet–Voronoi (DV) cell of the root lattice \(A_n\) in the form of the convex hull of an \(n\)-dimensional parallelotope with a vertex at 0 and its copies centrally symmetric with respect to 0 is given. Remarkable properties of this DV-cell are described, which manifest themselves when layers of the lattice \(A_n\) are superposed. It is shown that the one-parameter family of their metric forms runs through the cone of positivity from one boundary to the other, passing through four \(L\)-type domains.
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Grishukhin, V.P. Layer Superposition of the Root Lattice \(A_n\). Math Notes 109, 218–230 (2021). https://doi.org/10.1134/S0001434621010259
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DOI: https://doi.org/10.1134/S0001434621010259