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Article Dans Une Revue Canadian Journal of Mathematics Année : 2020

The weak order on Weyl posets

Résumé

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 which 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.
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Dates et versions

hal-02344060 , version 1 (03-11-2019)

Identifiants

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Joël Gay, Vincent Pilaud. The weak order on Weyl posets. Canadian Journal of Mathematics, 2020, 72 (4), pp.867-899. ⟨10.4153/S0008414X19000063⟩. ⟨hal-02344060⟩
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