This picture arises in the representation theory of the affine
sl3 and
of the affine symmetric group S3. Each
triangular tile represents an element of affine S3.
The colored tiles depict
the difference or quotient of the affine symmetric group by the
finite one. The dotted lines
show a projection that moves from the l = 3
setting to that of l = 2.
We are hoping this combinatorial projection is a shadow of a
deeper representation-theoretic phenomenon,
and will point the way to uncovering it.