On quotients of Coxeter groups under the weak order
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.
scientific article; zbMATH DE number 1956075
scientific article