Lorentzian lattices and E-polytopes

Adrian Clingher, Jae Hyouk Lee

Research output: Contribution to journalArticlepeer-review

Abstract

We consider certain En-type root lattices embedded within the standard Lorentzian lattice ℤn+1 (3 ≤ n ≤ 8) and study their discrete geometry from the point of view of del Pezzo surface geometry. The lattice ℤn+1 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)21.

Original languageEnglish
Article number443
JournalSymmetry
Volume10
Issue number10
DOIs
StatePublished - 2018

Keywords

  • Dual lattice
  • E-polytope
  • Gosset polytope
  • Lines
  • Lorentzian lattice
  • Root lattice
  • Weyl group

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