Subword complexes in Coxeter groups [article]

Allen Knutson, Ezra Miller
2003 arXiv   pre-print
Let (Π,Σ) be a Coxeter system. An ordered list of elements in Σ and an element in Π determine a subword complex, as introduced in our paper on Gröbner geometry of Schubert polynomials (math.AG/0110058). Subword complexes are demonstrated here to be homeomorphic to balls or spheres, and their Hilbert series are shown to reflect combinatorial properties of reduced expressions in Coxeter groups. Two formulae for double Grothendieck polynomials, one of which is due to Fomin and Kirillov, are
more » ... ed in the context of simplicial topology for subword complexes. Some open questions related to subword complexes are presented.
arXiv:math/0309259v1 fatcat:zkijscvdnzdpflyitigrvax27q