Lattice Congruences of the Weak Order

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

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