Subword Complexes and Nil-Hecke Moves
For a finite Coxeter group W, a subword complex is a simplicial complex associated with a pair (Q, ρ), where Q is a word in the alphabet of simple reflections, ρ is a group element. We describe the transformations of such a complex induced by nil-moves and inverse operations on Q in the nil-Hecke mo...
Main Author: | |
---|---|
Format: | Article |
Language: | English |
Published: |
Yaroslavl State University
2013-01-01
|
Series: | Моделирование и анализ информационных систем |
Subjects: | |
Online Access: | http://mais-journal.ru/jour/article/view/163 |
Summary: | For a finite Coxeter group W, a subword complex is a simplicial complex associated with a pair (Q, ρ), where Q is a word in the alphabet of simple reflections, ρ is a group element. We describe the transformations of such a complex induced by nil-moves and inverse operations on Q in the nil-Hecke monoid corresponding to W. If the complex is polytopal, we also describe such transformations for the dual polytope. For W simply-laced, these descriptions and results of [5] provide an algorithm for the construction of the subword complex corresponding to (Q, ρ) from the one corresponding to (δ(Q), ρ), for any sequence of elementary moves reducing the word Q to its Demazure product δ(Q). The former complex is spherical or empty if and only if the latter one is empty. The article is published in the author’s wording. |
---|---|
ISSN: | 1818-1015 2313-5417 |