Transactions of the American Mathematical Society

Author(s): Thomas Brady; Colum Watt
Journal: Trans. Amer. Math. Soc. 360 (2008), 1983-2005.
MSC (2000): Primary 20F55; Secondary 05E15
Posted: October 23, 2007
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Abstract: For a finite real reflection group

with Coxeter element $\gamma$ we give a case-free proof that the closed interval, $[I, \gamma]$ , forms a lattice in the partial order on

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

simplicial generalised associahedron, and we use this fact to give a new proof that the geometric realisation of this associahedron is a sphere.

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Thomas Brady
Affiliation: School of Mathematical Sciences, Dublin City University, Glasnevin, Dublin 9, Ireland
Email: tom.brady@dcu.ie

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