Subword complexes in Coxeter groups

摘要: Abstract Let ( Π , Σ ) be a Coxeter system. An ordered list of elements in and an element determine subword complex as introduced Knutson Miller (Ann. Math. (2) (2003), to appear). Subword complexes are demonstrated here homeomorphic balls or spheres, their Hilbert series shown reflect combinatorial properties reduced expressions groups. Two formulae for double Grothendieck polynomials, one which appeared Fomin Kirillov (Proceedings the Sixth Conference Formal Power Series Algebraic Combinatorics, DIMACS, 1994, pp. 183–190), recovered context simplicial topology complexes. Some open questions related presented.