Geodesic
The Weak Order on Weyl Posets
Canadian journal of mathematics, Tome 72 (2020) no. 4, pp. 867-899

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DOI

We define a natural lattice structure on all subsets of a finite root system that extends the weak order on the elements of the corresponding Coxeter group. For crystallographic root systems, we show that the subposet of this lattice induced by antisymmetric closed subsets of roots is again a lattice. We then study further subposets of this lattice that naturally correspond to the elements, the intervals, and the faces of the permutahedron and the generalized associahedra of the corresponding Weyl group. These results extend to arbitrary finite crystallographic root systems the recent results of G. Chatel, V. Pilaud, and V. Pons on the weak order on posets and its induced subposets.
DOI : 10.4153/S0008414X19000063
Mots-clés : weak order, finite Coxeter group, root system 
Gay, Joël; Pilaud, Vincent. The Weak Order on Weyl Posets. Canadian journal of mathematics, Tome 72 (2020) no. 4, pp. 867-899. doi: 10.4153/S0008414X19000063
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     title = {The {Weak} {Order} on {Weyl} {Posets}},
     journal = {Canadian journal of mathematics},
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     year = {2020},
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     number = {4},
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