10.1007/BF00383400
Abels, Herbert
Herbert
Abels
The geometry of the chamber system of a semimodular lattice
KLUWER ACADEMIC PUBL
1991
2010-04-29T13:30:39Z
2019-05-03T14:18:14Z
journal_article
https://pub.uni-bielefeld.de/record/1648931
https://pub.uni-bielefeld.de/record/1648931.json
In this paper geometric properties of the following metric space C are studied. Its elements are called chambers and are the maximal chains of a semimodular lattice X of finite height and its metric d is the gallery distance. We show that X has many properties in common with buildings. More specifically, Tits [17] has recently described buildings in terms of "Weyl-group valued distance functions". We consider the Jordan-Holder permutation pi(C, D) corresponding to a pair C, D of chambers and show that it has most properties of such a distance with values in the symmetric group.