Lattices in Finite Real reflection Groups

Thomas Brady, Colum Watt

Research output: Contribution to journalArticlepeer-review

Abstract

For a finite real reflection group, $W$, with Coxeter element $\gamma$ we give a uniform proof that the closed interval, $[I, \gamma]$ forms a lattice in the partial order on $W$ induced by reflection length. The proof involves the construction of a simplicial complex which can be embedded in the type W simplicial generalised associahedron.
Original languageEnglish
JournalarXiv: Combinatorics
DOIs
Publication statusPublished - 1 Jan 2008

Keywords

  • finite real reflection group
  • Coxeter element
  • lattice
  • partial order
  • reflection length
  • simplicial complex
  • generalised associahedron

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