In his article of 2019, Dyer states some conjectures about the weak order of a Coxeter group. Among them, one affirms that the extended weak order is a lattice and gives an algebraic-geometric characterization of the join of two elements in this poset. The first assertion has been recently proven for affine types by Barkley and Speyer. In this paper, we prove the second for Coxeter groups of type A and I.
Biagioli, R., Perrone, L. (2025). On a conjecture of Dyer on the join in the weak order of a Coxeter group.
On a conjecture of Dyer on the join in the weak order of a Coxeter group
Riccardo Biagioli;Lorenzo Perrone
2025
Abstract
In his article of 2019, Dyer states some conjectures about the weak order of a Coxeter group. Among them, one affirms that the extended weak order is a lattice and gives an algebraic-geometric characterization of the join of two elements in this poset. The first assertion has been recently proven for affine types by Barkley and Speyer. In this paper, we prove the second for Coxeter groups of type A and I.File in questo prodotto:
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