Cayley lattices of finite Coxeter groups are bounded
by
Nathalie Caspard
LACL, Université Paris 12 Val de Marne, 61 avenue du Général de Gaulle 94010 Créteil cedex, France
Coauthors: Claude LE CONTE DE POLY-BARBUT and Michel MORVAN

We prove that the Cayley lattices of finite Coxeter groups are bounded, i.e. that they can be constructed starting with the one-element lattice by a finite series of " interval doublings". This operation applies on a poset P and an interval I of P, and constructs a new "bigger" poset P'=P[I] by replacing in P the interval I with its direct product I*2 (where 2 is the two-element chain). This result uses the central concept of "reflection" of a Coxeter group and strengthens the algebraic property of semidistributivity satisfied by Coxeter lattices.

Date received: February 17, 2003