Highly Influenced

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@article{Reading2004LatticeCO, title={Lattice Congruences of the Weak Order}, author={Nathan Reading}, journal={Order}, year={2004}, volume={21}, pages={315-344} }

- Published in Order 2004
DOI:10.1007/s11083-005-4803-8

We study the congruence lattice of the poset of regions of a hyperplane arrangement, with particular emphasis on the weak order on a finite Coxeter group. Our starting point is a theorem from a previous paper which gives a geometric description of the poset of join-irreducibles of the congruence lattice of the poset of regions in terms of certain polyhedral decompositions of the hyperplanes. For a finite Coxeter system (W, S) and a subset K ⊆ S, let ηK : w → wK be the projection onto the… CONTINUE READING