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1 results

  • The Weak Order on Weyl Posets

  • Part of
  • Joël Gay, Vincent Pilaud
  • Journal:
    Canadian Journal of Mathematics / Volume 72 / Issue 4 / August 2020
    Published online by Cambridge University Press:
    29 January 2019, pp. 867-899
    Print publication:
    August 2020

  • 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.