Title

Lorentzian lattices and E-polytopes

Document Type

Article

Abstract

We consider certain E -type root lattices embedded within the standard Lorentzian lattice ℤ (3 ≤ n ≤ 8) and study their discrete geometry from the point of view of del Pezzo surface geometry. The lattice ℤ decomposes as a disjoint union of affine hyperplanes which satisfy a certain periodicity. We introduce the notions of line vectors, rational conic vectors, and rational cubics vectors and their relations to E-polytopes. We also discuss the relation between these special vectors and the combinatorics of the Gosset polytopes of type (n - 4) . n 21 n+1 n+1

Publication Date

1-1-2018

Publication Title

Symmetry

Volume

10

Issue

10

DOI

10.3390/sym10100443

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