@article{1648931,
abstract = {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.},
author = {Abels, Herbert},
issn = {0167-8094},
journal = {Order. A Journal on the Theory of Ordered Sets and its Applications},
keyword = {WEIL-GROUP VALUED DISTANCE FUNCTION, JORDAN-HOLDER PERMUTATION, SEMIMODULAR LATTICE, SCHUBERT SYMBOL, CHAMBER SYSTEM},
number = {2},
pages = {143--158},
publisher = {KLUWER ACADEMIC PUBL},
title = {{The geometry of the chamber system of a semimodular lattice}},
doi = {10.1007/BF00383400},
volume = {8},
year = {1991},
}