Lattices in Finite Real reflection Groups

Thomas Brady; Colum Watt

doi:10.21427/kzsd-1a33

Lattices in Finite Real reflection Groups

Thomas Brady, Colum Watt

Technological University Dublin

Research output: Contribution to journal › Article › peer-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 language	English
Journal	arXiv: Combinatorics
DOIs	https://doi.org/10.21427/kzsd-1a33
Publication status	Published - 1 Jan 2008

Keywords

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

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10.21427/kzsd-1a33Licence: CC BY-NC-SA

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title = "Lattices in Finite Real reflection Groups",

abstract = "For a finite real reflection group, \$W\$, with Coxeter element \$\textbackslash{}gamma\$ we give a uniform proof that the closed interval, \$[I, \textbackslash{}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.",

keywords = "finite real reflection group, Coxeter element, lattice, partial order, reflection length, simplicial complex, generalised associahedron",

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AB - 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.

KW - finite real reflection group

KW - Coxeter element

KW - lattice

KW - partial order

KW - reflection length

KW - simplicial complex

KW - generalised associahedron

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DO - 10.21427/kzsd-1a33

M3 - Article

JO - arXiv: Combinatorics

JF - arXiv: Combinatorics

ER -

Lattices in Finite Real reflection Groups

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Keywords

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