Non-crossing partition lattices in finite real reflection groups
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- by Thomas Brady and Colum Watt PDF
- Trans. Amer. Math. Soc. 360 (2008), 1983-2005 Request permission
Abstract:
For a finite real reflection group $W$ with Coxeter element $\gamma$ we give a case-free proof that the closed interval, $[I, \gamma ]$, forms a lattice in the partial order on $W$ induced by reflection length. Key to this is the construction of an isomorphic lattice of spherical simplicial complexes. We also prove that the greatest element in this latter lattice embeds in the type $W$ simplicial generalised associahedron, and we use this fact to give a new proof that the geometric realisation of this associahedron is a sphere.References
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Additional Information
- Thomas Brady
- Affiliation: School of Mathematical Sciences, Dublin City University, Glasnevin, Dublin 9, Ireland
- Email: tom.brady@dcu.ie
- Colum Watt
- Affiliation: School of Mathematical Sciences, Dublin Institute of Technology, Kevin St., Dublin 8, Ireland
- Email: colum.watt@dit.ie
- Received by editor(s): January 27, 2005
- Received by editor(s) in revised form: December 17, 2005
- Published electronically: October 23, 2007
- © Copyright 2007 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 360 (2008), 1983-2005
- MSC (2000): Primary 20F55; Secondary 05E15
- DOI: https://doi.org/10.1090/S0002-9947-07-04282-1
- MathSciNet review: 2366971