There is a homomorphism of the coroot lattice into the affine
Weyl group.

At least in principle, this can be computed by taking a fundamental
alcove F and translating it by an element d of the coroot lattice,
then
seeing what alcoves lie between F and F+d. It seems to me that
it would be desirable to be able to actually implement this.

Has anyone actually done this? (Anne maybe?)

Something like this was alluded to in this message of Nicolas:

http://groups.google.com/group/sage-combinat-devel/msg/59f0c1d620440240

If one has available the extended affine Weyl group, the
homomorphism will be defined on the whole coweight lattice.

Dan

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