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Bruhat intervals of length 4 in Weyl groups
KTH, Superseded Departments, Mathematics.
2003 (English)In: Journal of combinatorial theory. Series A (Print), ISSN 0097-3165, E-ISSN 1096-0899, Vol. 102, no 1, 163-178 p.Article in journal (Refereed) Published
Abstract [en]

We determine all isomorphism classes of intervals of length 4 in the Bruhat order on the Weyl groups A(4), B-4, D-4 and F-4. It turns out that there are 24 of them (some of which are dual to each other). Work of Dyer allows us to conclude that these are the only intervals of length 4 that can occur in the Bruhat order on any Weyl group. We also determine the intervals that arise already in the smaller classes of simply laced Weyl groups and symmetric groups. Our method combines theoretical arguments and computer calculations. We also present an independent, completely computerized, approach.

Place, publisher, year, edition, pages
2003. Vol. 102, no 1, 163-178 p.
Keyword [en]
Bruhat order, Bruhat intervals, Coxeter groups, Weyl groups, coxeter groups, subgroups
Identifiers
URN: urn:nbn:se:kth:diva-22447DOI: 10.1016/s0097-3165(03)00027-xISI: 000182429700011OAI: oai:DiVA.org:kth-22447DiVA: diva2:341145
Note
QC 20100525Available from: 2010-08-10 Created: 2010-08-10 Last updated: 2017-12-12Bibliographically approved

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