Lattices in Finite Real reflection Groups

Authors

Colum Watt, Technological University DublinFollow
Thomas Brady, Dublin City UniversityFollow

Document Type

Article

Rights

Available under a Creative Commons Attribution Non-Commercial Share Alike 4.0 International Licence

Disciplines

Pure mathematics

Publication Details

Non-crossing partition lattices in finite real reflection groups.

Trans. Am. Math. Soc. Vol. 360, No. 4, pp. 1983-2005 (2008).

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.

DOI

https://doi.org/10.21427/kzsd-1a33

Recommended Citation

Brady, T., & Watt, C. (2005). Lattices in finite real reflection groups. arXiv: Combinatorics. DOI: 10.21427/kzsd-1a33