Problem of the Week
Hilton Memorial Lecture
Björner and Wachs proved that under the weak order every quotient of a Coxeter group is a meet semi-lattice, and in the finite case is a lattice. We examine the case of an affine Weyl group and determine which quotients are lattices under the weak order. Our argument will involve the Shi arrangement of hyperplanes and shortest paths among Weyl alcoves.