On quotients of Coxeter groups under the weak order
type: Item
instance of: scholarly article
title: On quotients of Coxeter groups under the weak order
zbMATH Open document ID: 1025.20025
DOI: 10.1016/S0196-8858(02)00540-7
author: Debra J. Waugh
published in: Advances in Applied Mathematics
publication date: 2003-07-29T00:00:00Z
review text: Although Coxeter groups have fascinated mathematicians for many years, there are still many questions about them that need resolution. This paper contributes to the wealth of knowledge by resolving the following question: when does the quotient of an infinite Coxeter group form a lattice under the ordering \(x<y\) if and only if a reduced expression for \(x\) begins or ends a reduced expression for \(y\). The author has already shown that the quotient of an affine Weyl group by the corresponding finite Weyl group is a lattice, and here she confirms that this is all. To summarise she shows no quotient of an infinite non-affine Coxeter group is a lattice via the concept of ``forbidden configurations'', which a slick implementation of Maple is able to compute for all necessary cases.
Mathematics Subject Classification ID: 20F55
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 06A07
zbMATH DE Number: 1956075
zbMATH Keywords: non-affine Coxeter groups
zbMATH Keywords: hyperbolic Coxeter groups
zbMATH Keywords: lattices
zbMATH Keywords: forbidden configurations
zbMATH Keywords: affine Weyl groups
reviewed by: Stephanie van Willigenburg
describes a project that uses: Maple
MaRDI profile type: Publication
cites work: Generalized Quotients in Coxeter Groups
cites work: Q3998721
cites work: Bruhat lattices, plane partition generating functions, and minuscule representations
cites work: Q3748279
cites work: On the fully commutative elements of Coxeter groups
cites work: Some combinatorial aspects of reduced words in finite Coxeter groups
cites work: Upper bounds in affine Weyl groups under the weak order
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description: scientific article; zbMATH DE number 1956075