The geometry of the chamber system of a semimodular lattice
Abels, Herbert
WEIL-GROUP VALUED DISTANCE FUNCTION
JORDAN-HOLDER PERMUTATION
SEMIMODULAR LATTICE
SCHUBERT SYMBOL
CHAMBER SYSTEM
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.
KLUWER ACADEMIC PUBL
1991
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doc-type:article
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https://pub.uni-bielefeld.de/record/1648931
Abels H. The geometry of the chamber system of a semimodular lattice. <em>Order. A Journal on the Theory of Ordered Sets and its Applications</em>. 1991;8(2):143-158.
eng
info:eu-repo/semantics/altIdentifier/doi/10.1007/BF00383400
info:eu-repo/semantics/altIdentifier/issn/0167-8094
info:eu-repo/semantics/altIdentifier/wos/A1991GT45300004
info:eu-repo/semantics/closedAccess