The geometry of the chamber system of a semimodular lattice

Abels H (1991)
Order. A Journal on the Theory of Ordered Sets and its Applications 8(2): 143-158.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
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.
Stichworte
WEIL-GROUP VALUED DISTANCE FUNCTION; JORDAN-HOLDER PERMUTATION; SEMIMODULAR LATTICE; SCHUBERT SYMBOL; CHAMBER SYSTEM
Erscheinungsjahr
1991
Zeitschriftentitel
Order. A Journal on the Theory of Ordered Sets and its Applications
Band
8
Ausgabe
2
Seite(n)
143-158
ISSN
0167-8094
Page URI
https://pub.uni-bielefeld.de/record/1648931

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Abels H. The geometry of the chamber system of a semimodular lattice. Order. A Journal on the Theory of Ordered Sets and its Applications. 1991;8(2):143-158.
Abels, H. (1991). The geometry of the chamber system of a semimodular lattice. Order. A Journal on the Theory of Ordered Sets and its Applications, 8(2), 143-158. doi:10.1007/BF00383400
Abels, H. (1991). The geometry of the chamber system of a semimodular lattice. Order. A Journal on the Theory of Ordered Sets and its Applications 8, 143-158.
Abels, H., 1991. The geometry of the chamber system of a semimodular lattice. Order. A Journal on the Theory of Ordered Sets and its Applications, 8(2), p 143-158.
H. Abels, “The geometry of the chamber system of a semimodular lattice”, Order. A Journal on the Theory of Ordered Sets and its Applications, vol. 8, 1991, pp. 143-158.
Abels, H.: The geometry of the chamber system of a semimodular lattice. Order. A Journal on the Theory of Ordered Sets and its Applications. 8, 143-158 (1991).
Abels, Herbert. “The geometry of the chamber system of a semimodular lattice”. Order. A Journal on the Theory of Ordered Sets and its Applications 8.2 (1991): 143-158.