On inversion sets and the weak order in Coxeter groups

被引：10

作者：

Hohlweg, Christophe ^{[1
,2
]}

Labbe, Jean-Philippe ^{[3
]}

机构：

[1] Univ Quebec, LaCIM, CP 8888 Succ Ctr Ville, Montreal, PQ H3C 3P8, Canada

[2] Univ Quebec, Dept Math, CP 8888 Succ Ctr Ville, Montreal, PQ H3C 3P8, Canada

[3] Hebrew Univ Jerusalem, Einstein Inst Math, IL-91904 Jerusalem, Israel

来源：

EUROPEAN JOURNAL OF COMBINATORICS | 2016年 / 55卷

基金：

加拿大自然科学与工程研究理事会;

关键词：

AFFINE ROOT SYSTEMS; SORTABLE ELEMENTS; CAMBRIAN LATTICES; CONJUGACY;

D O I：

10.1016/j.ejc.2016.01.002

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article, we investigate the existence of joins in the weak order of an infinite Coxeter group W. We give a geometric characterization of the existence of a join for a subset X in W in terms of the inversion sets of its elements and their position relative to the imaginary cone. Finally, we discuss inversion sets of infinite reduced words and the notions of biconvex and biclosed sets of positive roots. (C) 2016 Elsevier Ltd. All rights reserved.

引用

页码：1 / 19

页数：19

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