---
_id: '1648931'
abstract:
- lang: eng
text: 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.
article_type: original
author:
- first_name: Herbert
full_name: Abels, Herbert
id: '10478'
last_name: Abels
citation:
ama: 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.
angewandte-chemie: H. Abels, “The geometry of the chamber system of a semimodular
lattice”, *Order. A Journal on the Theory of Ordered Sets and its Applications*,
**1991**, *8*, 143-158.
apa: 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
apa_indent: 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

bio1: '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.'
chicago: 'Abels,
Herbert. 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.

'
default: 'Abels H (1991)

*Order. A Journal on the Theory of Ordered Sets
and its Applications* 8(2): 143-158.'
dgps: 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. KLUWER ACADEMIC PUBL. doi:10.1007/BF00383400.

frontiers: 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.
harvard1: 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.
ieee: ' 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.'
lncs: ' 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).'
mla: '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.'
wels: '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.'
date_created: 2010-04-29T13:30:39Z
date_updated: 2019-05-03T14:18:14Z
department:
- _id: '10020'
doi: 10.1007/BF00383400
external_id:
isi:
- A1991GT45300004
intvolume: ' 8'
isi: 1
issue: '2'
keyword:
- WEIL-GROUP VALUED DISTANCE FUNCTION
- JORDAN-HOLDER PERMUTATION
- SEMIMODULAR LATTICE
- SCHUBERT SYMBOL
- CHAMBER SYSTEM
language:
- iso: eng
page: 143-158
publication: Order. A Journal on the Theory of Ordered Sets and its Applications
publication_identifier:
issn:
- 0167-8094
publication_status: published
publisher: KLUWER ACADEMIC PUBL
quality_controlled: '1'
status: public
title: The geometry of the chamber system of a semimodular lattice
type: journal_article
user_id: '67994'
volume: 8
year: '1991'
...