Subword complexes in Coxeter groups
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- 作者：Knutson ; Allen ; Miller ; Ezra
- 关键词：20F55 ; 13F55 ; 06A08 (Primary) ; 05E05 (Secondary) ; Coxeter group ; Reduced composition ; Reduced word ; Reduced expression ; Subword ; Simplicial complex ; Shellable ; Vertex-decomposable ; Hilbert series ; Grothendieck polynomial
- 刊名：Advances in Mathematics
- 出版年：2004
- 出版时间：May 1, 2004
- 年：2004
- 卷：184
- 期：1
- 页码：161-176
- 全文大小：206 K
文摘
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.