Lattices in finite real reflection groups

Details Lattices in finite real reflection groups Lattices in finite real reflection groups

2005-01-28

arxiv.org/abs/math/0501502v1

Mathematics

Combinatorics

29 pages, 3 figures

Scientific paper

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.

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