Quotients of Coxeter Groups under the Weak Order

Debra J. Waugh

To appear at Formal Power Series and Algebraic Combinatorics (FPSAC01), Tempe, Arizona (USA), May 20-26, 2001


We consider quotients of finitely generated Coxeter groups under the weak order. Our result is that the quotient of an affine Weyl group by the corresponding finite Weyl group is a lattice, and that up to isomorphism, these are the only quotients of infinite Coxeter groups that are lattices. In this paper, we restrict our attention to the non-affine case; the affine case appears elsewhere. We reduce to the hyperbolic case by an argument using induced subgraphs of Coxeter graphs. Within each quotient, we produce a set of elements with no common upper bound, generated by a Maple program. We are often able to use the same set repeatedly because the sets satisfy the following conjecture: if a set of elements does not have an upper bound in a particular Coxeter group, then it does not have an upper bound in any Coxeter group whose graph can be obtained from the graph of the original group by increasing edge weights.

Server START Conference Manager
Update Time 23 Feb 2001 at 08:48:03
Maintainer maylis@labri.u-bordeaux.fr.
Start Conference Manager
Conference Systems