Bases for the Bruhat–Chevalley Order on All Finite Coxeter Groups

✍ Scribed by Meinolf Geck; Sungsoon Kim

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 403 KB
• Volume: 197
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.1997.7096

✦ Synopsis

Let W, S be any finite Coxeter system and F the Bruhat᎐Chevalley Ž .

Ž . order on W. We denote by Base W and BiGr W the base and the set of all bi-grassmannians, respectively. For s, t g S we let s W t be the subset of Ž . Ž . Ä 4 Ž . Ä 4 BiGr W consisting of all w g W such that L L w s s and R R w s t . Thus, we have BiGr W s s W t .

Ž .