Subword complexes in Coxeter groups

Details Subword complexes in Coxeter groups Subword complexes in Coxeter groups

2003-09-16

arxiv.org/abs/math/0309259v1

Mathematics

Combinatorics

14 pages. Final version, to appear in Advances in Mathematics. This paper was split off from math.AG/0110058v2, whose version

Scientific paper

Let (\Pi,\Sigma) be a Coxeter system. An ordered list of elements in \Sigma and an element in \Pi determine a {\em subword complex}, as introduced in our paper on Gr\"obner 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 recovered in the context of simplicial topology for subword complexes. Some open questions related to subword complexes are presented.

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