Subword complexes in Coxeter groups


Journal Article

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 Knutson and Miller (Ann. of Math. (2) (2003), to appear). 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 appeared in Fomin and Kirillov (Proceedings of the Sixth Conference in Formal Power Series and Algebraic Combinatorics, DIMACS, 1994, pp. 183-190), are recovered in the context of simplicial topology for subword complexes. Some open questions related to subword complexes are presented. © 2003 Elsevier Inc. All rights reserved.

Full Text

Duke Authors

Cited Authors

  • Knutson, A; Miller, E

Published Date

  • May 1, 2004

Published In

Volume / Issue

  • 184 / 1

Start / End Page

  • 161 - 176

International Standard Serial Number (ISSN)

  • 0001-8708

Digital Object Identifier (DOI)

  • 10.1016/S0001-8708(03)00142-7

Citation Source

  • Scopus